Date: 202109
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: VMC
Weather elements / visibility: Rain
Light: Daylight
Aircraft: A319
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Climb; Initial Climb
Airspace: Class B ZZZ
ATC / advisory: TRACON ZZZ; Tower ZZZ
Aircraft component: Emergency Exit
Component problem: Improperly Operated; Malfunctioning
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Human factors: Distraction; Troubleshooting
Anomaly: Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Maintenance; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Flight Crew Landed As Precaution; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Returned To Departure Airport; General Flight Cancelled / Delayed; General Maintenance Action
Contributing factors: Aircraft; Human Factors; Procedure
Primary problem: Procedure

Narrative: Our aircraft came to the gate directly from the maintenance hangar.  We were given [Runway] XR for take off. I was the Pilot Monitoring (PM). Due to wind shear alerts on the approach; and WX moving toward the field; we elected to do a TOGA take off. We were on the ZZZZZ Departure; but were given a heading immediately after takeoff to avoid a cell. Approximately 5-7 min after takeoff; and cleared to climb to 16k feet; we got a 'DOOR  L EMER EXIT' EICAS message. The First Officer (FO) declared it was his aircraft and we identified the need to level off at 10k. I notified Departure; and they gave us clearance to stop climb at 10k. I told him we were troubleshooting and we would need to return to ZZZ. We requested priority. The FO took over the radio; and I was tying to determine the problem and keep the passengers and flight attendants appraised of the situation. I briefed the flight attendants a couple of times on ALL; and made a PA to the passengers. The number 1 Flight Attendant told me that a cover for that over wing emergency exit had fallen off. I notified the company through ACARS that we were returning to ZZZ and they acknowledged. Meanwhile; the weather had hit the airport; and they asked us if we wanted to land with a tailwind; or if we wanted to wait for the field to be turned around. (Landing west now)We told them we would prefer to land with a headwind. They told us to expect the RNAV to [Runway] XX because the ILS was not up yet.  We accomplished the descent checklist and set up for the RNAV. Approach later told the plane ahead of us that the ILS was working now; so we set up for that while being vectored. The weather was not optimal - there was a strong rain column over the field; about 1/2 way down Runway XX; but we had a good visual on the field.  We discussed the need for a hard go-around if needed.  After an outstanding landing from the right seat; we were met by possibly every priority vehicle at ZZZ as we taxied clear of [Runway] XX. They checked that we did not need any further assistance; and the on scene commander followed us all the way to the recovery gate.  After evaluation by maintenance; we were told that the cover that had fallen off is held in place by a rather flimsy metal clip. There is a magnet on the cover; and when the cover is removed; it causes the alarm that we received. He said that the covers are routinely removed when the plane is in the hanger; and that they can sometimes get loose. They eventually adjusted the clips for both over wing exits and returned the aircraft to service. We flew it to ZZZ1 and back with no further issues.I was told that; had the handle been pulled on the emergency exit; due to the plug nature of the exit; the hatch would most likely not have moved. The slide; however; would have deployed. This would have caused major controllability issues. Additionally; after discussing it with safety; I was told that this is not a common problem; but it is one that could use greater awareness for pilots. The metal clip holding the emergency exit cover in place was either loose or had not been seated properly.  Had the cover fallen off at altitude; the EICAS would have asked for an emergency descent to 10k; which would; obviously be very dramatic. Our air interrupt and any further similar events could be avoided if the pilots were trained to replace the cover before as step one in trouble shooting.




Synopsis: Captain reported an Air Turn Back caused by an EICAS message DOOR L EMER EXIT on climb out.