The Twilight star filed suit against McMahon's RV last month (Aug10) claiming the firm failed to deliver a vehicle for use on the set of his new movie Abduction on time.
Company owner Brent McMahon responded by calling on the teenager to settle the legal dispute with a push-up contest, and offered to hand over $40,000 (£26,000) to Lautner if the actor won the challenge - but would give the cash to charity if he failed.
But the proposal has been rejected by Lautner's legal team.
The actor's lawyer Robert Barta says, ""McMahon RV's response to our client's legitimate claim further demonstrates the lack of professionalism that Mr. McMahon, his company, and his employees have exhibited from the outset, and that compelled the filing of this lawsuit in the first place.""
However, Barta said Lautner did ""welcome the opportunity for him to resolve the matter by making a $40,000 donation to the charity of Mr. Lautner's choice.""