Your post suggests that you have used these pots. Pots that are used are typically exposed to chemicals that are lethal to fish (pesticides, herbicides, fertilizer, etc.) And terra cotta (clay) absorbs those things along with minerals as it absorbs the water. The white stuff is residue from salts and chemicals that caked up on the pots as it was being used.
Terra cotta pots are cheap. Walmart sells them for under $3.
Honestly, I have been a tightwad since age 6, but I can't think of a reason to risk placing used terra cotta pots in an aquarium. New ones, yup. Used nope.
Even if the odds are 1 in 100, I'm for getting new ones.
Ah should have been more clear they have only ever been used in aqariums. But good looking out.