Okay, I've spent the last hour and more investigating the half-life of caffeine and decaffeination methods and your best bet is to simply soak, rinse and repeat using fresh water which is one method used for tea and coffee decaffeination only that in those cases instead of throwing the water away the caffeine is removed from the water by activated carbon, then the residue from evaporating the water is added back to the tea or coffee to put the taste back. The other methods won't be suitable for home use unfortunately but being extremely soluble in water you can remove all of the caffeine quite easily just soaking in clean water a few times.
Edit - A couple of things, tea contains about half of the amount of caffeine as coffee, but still a substantial amount so you would be best to soak the tea painted nests too. Also, caffeine is not listed as highly toxic to insects but does have adverse effects on some, the effects of caffeine are exaggerated because they can't metabolise and eliminate it very well whereas it is listed as being toxic to birds, dogs and cats. So I don't think a bit of caffeine will kill the ants directly, but they might behave strangely.
Edited by DaveJay, November 27 2018 - 10:53 PM.