When you buy a traveler's check from a bank or agency, before you leave you have to sign every check. Then, when you cash a check, you have to sign again. Your signature can be examined to prove that you are the same person that bought the check.
If you suspect the check is a stolen one, ask to see the ID and signature of the presenter. If the check belongs to them then their name should be the same as the first signature on the check.
If a check has both signatures filled in and they are both the same, then it should be honored. It may be that it was handed over in payment for some service.