Is this in a shower? Around a tub?
If the tiles fell off a damp wall, my guess is that the wall is green board or other gypsum tile backer board. Once this wall gets water in it (it’s damp), the only thing you can do is remove the bad area, which will be much larger than the area where the tile fell off of, check the condition of the wall studs behind the wallboard, replace the wallboard with new moisture resistant tile backer (or better yet, re-do the entire shower or tub walls with a cementitious tile backer board such as DuraRock or WonderBoard and get rid of the drywall as that only leads to long term problem, as you are seeing), then replace the tile.
If this is only a very small area (which is unlikely), you may be able to scrape the grout and mastic / thin set off the back and edges of the tile and let the tile dry thoroughly. This is a very tedious and time consuming project and I would only advise it if the tile are special tiles. I did this once when a client wanted to re-do a shower which was done with original hand made and hand painted tiles. We were fortunate in that we only broke about 3 of those tiles. But in trying to rush the drying process for the owner, we heated them slightly in the oven. One batch was left in a little to long and they came out darker (the best description would be burnt looking) than they went in. In the end, the owner was glad they could save these custom tiles, but said they would probably never do it again. (I know, don’t ask why anyone would use expensive hand made tiles over MR drywall instead of putting them over DuraRock tile backer board. Wasted expenditure of money.)
[Edited by Jerry Peck on 21 December 2000]