Depends on how old the house is and if you live in the US, what the building codes are will determain the mold. If there has been water getting behind the grout, but there is hardi-rock (cement board) behind the tile, then chances are there isnt any mold, just re-grout then put a sealer on the grout. If there is only drywall, then tear off the tile, replace the drywall behind the tile with hardi-rock, re-tile, re-grout.
But, you might be in luck as the tub may have a lip tucked behind the tile to catch water that may leak. look at the pic below to see the lip Im refering to:

If there is mold behind there, poor mans way to help get rid of it, bleach the hell out of it. There are mold killers on the market, look at there main ingredient and its bleach, but without the smell, so buy lemon or orange scented bleach.
This may be the time you and the spouse may want to rethink tile selction as well. tile is fairly cheap. If your going to replace just some of the tiles, chances are the color of the new tile wont match the color of the old. Buy enough new, from the same manufactures lot code, so the pigments were all blended at the same time and are 99% uniform with color. Mix all your grout at the same time for consistancy. Same thought process for grout as well, it may say Beige on the package, but beige pigment from 20 yrs ago may not be the same beige today.

Good Luck,
Fordman