I just stumbled across something unexpected in my Latin dictionary. The entry is:
grates, f. pl. thanks; grates agere, to express thanks; ~ habere, to feel gratitude.
Now, for as long as I can remember, I've used the phrase gratias tibi ago
to thank someone. Looking below at "gratias," I see that the same expressions with "agere" and "habere" are used with "gratias" and "grates" alike, meaning essentially the same thing, it would appear.