A restrictive endorsement limits the use of a financial instrument (usually a check). The result of a restrictive endorsement is that a financial instrument is no longer a negotiable instrument that can be passed from the stated payee to a third party. An example of a restrictive endorsement is the "For Deposit Only" stamp used by most companies on the back of a received check. This stamp effectively limits further action on the check by the stated payee to only being able to deposit it.
A customer may send a supplier a check payment, on which is written the words "in full payment of account" or similar terms. This is not precisely a restrictive endorsement, since it is not restricting the further negotiability of the check. However, it may have a substantial impact on the ability of the supplier to obtain payment on any remaining unpaid balance on the customer's account, since depositing the check may be considered acceptance of the terms added to the check. The decision process when you receive such a check is:
Discuss the matter with legal counsel to see how it is impacted by applicable laws.
If you were about to write off the account balance (thereby assigning zero value to the unpaid amount), then it probably makes sense to deposit the check and write off the remaining balance.
If you intend to pursue full payment, then return the check to the customer. Do not deposit it.
If you use a bank lockbox to deposit all incoming checks, then impose a procedure where the bank staff does not deposit any checks containing restrictive endorsements, and instead forwards them to the company for review.