It's possible some minor damage may have occurred, but not very likely-nor very damaging. Were it as bad as he made it sound, the unit would not be running at this point. The concerns with overcharging aren't pressures as much as fear of liquid getting back to the compressor in the vapor line-this takes out the valves in the compressor, for as we all know-you can't compress a liquid! It would also help to know that overcharging does not result in colder air, but conversely-it kills the dehumidification resulting in a "sticky" cool.
Given that the compressor is running now, you should be OK for at least a few more years. Don't call the old company back (there's a shocker, huh?), but also be leary of the new company as well. It sounds like they're planting the "seed" of thought for replacement of a system that may not need replacing.
Judging from your post, the thermostat was probably miswired and the refrigerant charge was out of kilter (definitely the mark of a "home warranty" technician) as you said they didn't do anything but remove refrigerant. Keep in mind that home warranty companies have signed on to get work and they offered it for the lowest price to the warranty company. You get what you don't pay for! From my experience-home warranties are a joke.
The best thing you can do at this point is:
Change filters *MONTHLY*
Clean outdoor coils annually
Clean evaporator (indoor) coils as needed-a good filter will prevent this!
Clear and clean condensate pan and line annually
Check contactor on outdoor unit annually-replace when points are burnt.
Check blower wheel and motor. Wipe motor, clean blower wheel if it's full of dirt-this will make the motor run cooler, provide more air flow, keep the wheel in balance, and make the entire unit run much longer and more efficiently.
A couple of simple facts to live by.
1. If the A/C mechanic rings your doorbell with a tank of R-22 in his hand-throw him out. A properly installed A/C or Heat Pump will *never* need refrigerant unless the line or coil is punctured/leaking. If you should have to add refrigerant (R410A or R22), the next question should be "where's the leak and how do I fix it?". Also note that refrigerant leaving the system takes the compressor oil with it as they are extremely miscible, and left alone a leak will eventually starve a compressor of lubrication. 85-95 percent of our calls are electrically related-not refrigerant.
Every manufacturer (without exception) recommends AT LEAST 10 to 15 minutes of compressor runtime before checking pressures/superheat/subcool and another 10-15 minutes wait time between additional charges, so charging a system *properly* should take a minimum of 30-45 minutes-not 15. That's called "gas 'n go" and typically occurs around quitting time. Especially on Friday. ; )
And finally... again-Home Warranties are a joke. Spend your money more wisely-say on a bouquet for your wife or girlfriend.