If you used medication, I wouldn’t put it back in the display tank. If you’re only using it for a quarantine tank, I’d think some water with a touch of vinegar would do the trick. You could always put it in a little ziploc bag to store. Or you could just pitch it to be extra careful. They’re pretty cheap.
Letting it dry thoroughly (use a fan) is the best way to disinfect for reuse. You can clean it using a mild vinegar:water solution, but be careful not to get any on the yellow part (use a q-tip).
After being cleaned/disinfected, I like to store them in a jar with RODI to keep the indicator fresh. Put the jar in a closet or something, to prevent light from causing algae to grow on the badge.