From your title, it's the indoor unit that is making the noise? Could be a whole host of things! I'm assuming the unit is new enough that it doesn't have a belt-drive blower wheel - please post the make and model numbers of the indoor and outdoor units.

I think you may need to get the company back that serviced the unit before you bought the house.

Screeching from an indoor unit is most likely either a belt (that would have to be an older unit) or most likely it is a direct drive blower from a modern residential air handler and it is a faulty bushing/bearing in the assembly or motor itself.
I would have to hear the noise, I have heard TXV scream too, and that is a bit tougher of a fix.

Thanks for the direction. I'm going to call the warranty company and have them come out. But now I know to expect them to mention a belt.