Anita - there are 2 issues with termites....................1. whether it's an active termite infestation.... and/or
2. whether there is any damage, structural or otherwsie, caused by the termites.
In regard to the first issue - know that houses can be treated....often holes are drilled aorund the exterior of the home, and chemicals used............homeowners are then given a warranty , usually for one year. Termites are all over the place, and not an unusual occurance - I wouldn't let that stop me from buying a home. Once treated, the problem is gone!
In regard to any damage done by termites - that, too can be corrected. You need to make sure the inspector can identify what damage has been done.....some damage may be minor, maybe aroiund the frame of the garage or a doorway, some damage may deal with more significant structural issues (beams), and may take a specialty carpenter's expertise to correct. Make sure the right expert is called in.
In any event............all of the above can and should be addressed by the seller. You will then receive a "clean bill of health" from the exterminator and for any carpentry work done.
I am sure a NY agent will come along who can give you a few names of companies to call.