A few months ago, I refinished 2 small tables with delicate inlay, but the inlay was not lifting, cracking or had any defects. I am not aware of any product that would assist your stripping of the piece and not affect your damaged inlay. So, I'm suspecting you will have to manually strip those delicate areas, i.e., gently sand (guage your own agressiveness) those areas with 220 grit sand paper, until the finish is removed.
Prior to sanding, I would try to reattach the loose or lifting pieces of inlay.... stabilize them, before attempting to work on them. If possible, insert new inlay where there are missing pieces.
Without seeing exactly what you have, there, I'm not sure what more I can suggest. At times, I've had problems inserting pics here, also. Maybe place the pics in your gallery, here. Post a link to another gallery (Photostream, Flickr) or email them.
Why has the inlay lifted or separated and is missing from the base wood, or can you determine? Moisture? Old glue has simply failed? Was the damage done as a result of some direct physical trauma to the table? Direct sunlight damage? Maybe some clue to any of these, or a combination of, may help determine a schedule for repair.