Now you've got me thinking about it. Time to nerd out, I guess, haha.

From an algebraic perspective, it would be whatever "undoes" a thank you.

From a logic perspective, it would be something that is the complement of a thank you, and contradicts a thank you given ty ∧ ¬ty or is a tautology when ty ∨ ¬ty.

"Welcome" doesn't seem to quite fit for either of those cases. "Not thank you" or "ungrateful" do indeed seem closer.