I don't think you have a lot of traction to this and here's why: If you were fired for failing to disclose a criminal conviction on your employment application to the contractor that you were asked to disclose in the application it really does not matter how they found out about it later, the fact is you lied on the application in their view so the termination of employment was reasonable and lawful. Home Depot may have in fact illegally done a background check but you will have no basis for damages against them for doing so since again, the termination was lawful and reasonable.
Hope you've found better employment and I agree someone has way too much time on their hands. I hope they think it's funny they are merely causing the issue of child molestation to not be taken seriously, in fact with that in mind it's not out of the imagination that they are in fact the one who molests children. Trolls suck, the only thing to do is ignore them.
I voted neutral on the complaint because I think Home Depot's actions were wrong but not enough to validate the complaint. Hope that makes sense.