Exhibit 10.5

EXECUTION VERSION

AMENDMENT TO THE WARRANT AGREEMENT

This Amendment to the Warrant Agreement (this “Amendment”), dated as of
February 28, 2019, is made, subject to the condition on effectiveness below, by
and between Affinion Group Holdings, Inc., a corporation organized under the
laws of the State of Delaware (the “Company”), American Stock Transfer & Trust
Company, LLC, a limited liability trust company organized under the laws of the
State of New York (the “Warrant Agent”), and the Holders of two-thirds of the
outstanding Warrants. Capitalized terms used and not defined herein shall have
the meaning ascribed thereto in the Warrant Agreement (as defined below).

WHEREAS, the Company and the Warrant Agent had entered into that certain Warrant
Agreement, dated as of May 10, 2017 (the “Warrant Agreement”);

WHEREAS, in connection with the exchange offer (the “Exchange Offer”), rights
offering and other transactions contemplated by the Support Agreement, the
Company desires to amend the terms of the Warrant Agreement to cause the
Warrants to be mandatorily exercised into shares of Common Stock in cashless
exercises prior to a merger of AGHI Merger Sub, Inc., a wholly owned subsidiary
of the Company, with and into the Company (the “Merger”);

WHEREAS, pursuant to Section 14 of the Warrant Agreement, amendments to the
Warrant Agreement require the written consent of (i) the Company, (ii) the
Warrant Agent and (iii) the Holders of two-thirds of the outstanding Warrants;
and

WHEREAS, the undersigned Holders hold two-thirds of the outstanding Warrants.

NOW, THEREFORE, in consideration of the covenants and agreements contained
herein and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties agree as follows:

1.    Amendments to the Warrant Agreement

(a)    Section 4(b) – Adjustments – Reorganization, Reclassification,
Consolidation, Merger or Sale of Assets. Section 4(b) of the Warrant Agreement
is hereby amended and restated as follows:

Mandatory Exercise Immediately prior to the Consummation of the Merger. Subject
to and immediately prior to consummation of the Merger, without further action
on behalf of the Holders, each Warrant shall be mandatorily exercised in full
pursuant to a Cashless Exercise in accordance with Section 3(a)(ii)(C). Any and
all requirements set forth in Section 3(a) regarding the delivery of the Warrant
Exercise Documentation and any other right of the Company to restrict the
exercise of the Warrants in connection with the Merger shall be deemed to have
been waived by the Company and the Warrant Agent. The Company shall be solely
responsible for any calculations of the Cashless Exercise under this
Section 4(b), and upon the completion of such Cashless Exercise the Company will
direct the Warrant Agent of the issuance of new

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Common Stock. Notwithstanding anything in Section 3(b) to the contrary, the
Company shall not be required to deliver certificates in respect of the Common
Stock validly issued upon exercise of any Warrant pursuant to this Section 4(b)
and such Common Stock shall be held in book-entry form on the transfer books of
the Company.

(b)    Section 20 – Termination. Section 20 of the Warrant Agreement is hereby
amended and restated as follows:

This Agreement shall terminate upon the earlier of (i) one day after the end of
the Exercise Period or, if and to the extent applicable, the delivery by the
Company to the Holders of all Common Stock and other securities or property in
respect of all Warrants duly exercised during the Exercise Period, (ii) when all
Warrants have been exercised upon the delivery to the Holders of all Common
Stock and other securities or property in respect of all Warrants duly exercised
and (iii) when all Warrants have been exercised and/or cancelled.
Notwithstanding the foregoing, Section 13(b) shall survive the termination of
this Agreement and the resignation or removal of the Warrant Agent.
Notwithstanding any Warrant Certificates evidencing the issuance of Common
Stock, the Warrants shall be terminated, cancelled and void after the Expiration
Date.

(c)    Section 25 – Definitions – Definition of “Expiration Date”. The
definition of “Expiration Date” in Section 25 of the Warrant Agreement is hereby
amended and restated as follows:

“Expiration Date” means immediately prior to the consummation of the Merger and
following the mandatory exercise of all Warrants pursuant to Section 4(b)
herein.

(d)    Section 25 – Definitions. Section 25 of the Warrant Agreement is hereby
amended by adding the following definitions in the appropriate places:

“Merger” means the merger of AGHI Merger Sub, Inc., a Delaware corporation and
wholly owned subsidiary of the Company, with and into the Company, with the
Company as the surviving entity, as more fully described in the Support
Agreement.

“Support Agreement” means that certain support agreement, dated on or about
February 28, 2019 (as amended or supplemented from time to time), by and among
the Company and certain of its subsidiaries that are signatories thereto and the
investors and lenders that are from time to time signatories thereto.

2.    Waivers. The undersigned waive any right to notice under Section 24 of the
Warrant Agreement with respect to the Merger or any transaction contemplated by
the Support Agreement.

3.    Miscellaneous. This Amendment and the Warrant Agreement contain the
complete agreement among the Company and the undersigned and supersede any prior
understandings, agreements, letters of intent, or representations by or among
such parties, written

 

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or oral, to the extent they relate to the subject matter hereof. Except as
specifically amended hereby, the Warrant Agreement shall remain in full force
and effect. This Amendment may be executed in multiple counterparts with the
same effect as if all signing parties had signed the same document. All
counterparts shall be construed together and constitute the same instrument.
This Amendment, to the extent signed and delivered by means of a facsimile
machine or electronic delivery (i.e., by email of a PDF signature page), shall
be treated in all manner and respects as an original agreement or instrument and
shall be considered to have the same binding legal effect as if it were the
original signed version thereof delivered in person. THIS AMENDMENT SHALL BE
CONSTRUED AND ENFORCED IN ACCORDANCE WITH, AND THE RIGHTS OF THE PARTIES SHALL
BE GOVERNED BY, THE LAWS OF THE STATE OF DELAWARE APPLICABLE TO AGREEMENTS MADE
AND TO BE PERFORMED ENTIRELY WITHIN SUCH STATE.

4.    Effectiveness. The effectiveness of this Amendment shall be conditioned on
the consummation of the Exchange Offer. In the event that the Exchange Offer is
not consummated, this Amendment shall automatically be void ab initio and have
no force or effect.

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IN WITNESS WHEREOF, the undersigned have executed this Amendment to be effective
as of the date first written above.

 

THE COMPANY: AFFINION GROUP HOLDINGS, INC. By:  

/s/ Gregory S. Miller

Name:   Gregory S. Miller Title:   Executive Vice President, Chief Financial
Officer and Chief Operating Officer

 

[Signature Page to Warrant Agreement Amendment]

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THE WARRANT AGENT: AMERICAN STOCK TRANSFER & TRUST

COMPANY, LLC

By:  

/s/ Michael Legregin

  Name:   Michael Legregin   Title:   Senior Vice President

 

[Signature Page to Warrant Agreement Amendment]

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WARRANT HOLDERS:

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METRO SPV LLC By:  

/s/ Andrew Hawkins

  Name:   Andrew Hawkins   Title:   Authorized Signatory Warrants:   967,660  

 

[Signature Page to Warrant Agreement Amendment]

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ELLIOTT ASSOCIATES, L.P. By: Elliott Capital Advisors, L.P., as general partner
By: Braxton Associates, Inc., as general partner By:  

/s/ Elliot Greenberg

  Name:   Elliot Greenberg   Title:   Vice President Warrants: 682,187

 

[Signature Page to Warrant Agreement Amendment]

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ELLIOTT INTERNATIONAL, L.P. By: Hambledon, Inc., its General Partner By: Elliott
International Capital Advisors Inc., as        attorney-in-fact By:  

/s/ Elliot Greenberg

  Name:   Elliot Greenberg   Title:   Vice President Warrants: 682,187

 

[Signature Page to Warrant Agreement Amendment]