If (s)he were to try and settle the dispute, it cannot be used against the defendant in court to prove negligence or wrongdoing. Ironically, this is so that people will be willing to settle disputes out of court, instead of clogging the court system with tons of suits.
So, giving the money back, in an attempt to settle the dispute, does not enable further suit.
Rule 408. Compromise and Offers to Compromise
(a) Prohibited uses.—Evidence of the following is not admissible on behalf of any party, when offered to prove liability for, invalidity of, or amount of a claim that was disputed as to validity or amount, or to impeach through a prior inconsistent statement or contradiction:
(1) furnishing or offering or promising to furnish or accepting or offering or promising to accept a valuable consideration in compromising or attempting to compromise the claim
Those are the Federal rules. They vary from state to state, but most are pretty close.
Does "the claim" here mean "anything people were arguing about", or does it specifically mean a lawsuit which had been filed?
If you're worried about ways settlement offers can potentially be used against you, remember that the rule only bars using such evidence for the purpose of proving liability. As long as its offered for some other purpose, it can be allowed in. And once a jury hears the evidence, in practice it doesn't really matter for what purpose they were told to consider it.