The phrase 'without prejudice' means literally, without prejudicing the legal rights of the person writing the letter despite the contents of the letter.
A LOD could contain an offer to repay the money in instalments and at a lower interest rate. Using the phrase 'without prejudice' means that if the letter's recipient declines to comply, the issuer can still go to court and enforce their legal rights for repayment of the whole amount at the original interest rate without repeating the offer of staged payments.
'Without prejudice' communications can be complex, and this label needs to be used by an experienced lawyer.