On quality guitars, the fret markers are held in place with hide glue; this is a glue that softens when heated, so that parts can be removed for repair or replacement without damaging the surrounding wood. Mother-of-pearl markers can be heated with a small soldering iron, but this technique won't work with acrylic or celluloid markers, which will melt or burn under intense heat. Acrylic markers can be removed, but they must be heated more slowly and carefully.
Lay the guitar on its back with a rolled up towel under the neck; this will keep the guitar level and stable when pressure is placed on the fingerboard.
Heat the acrylic marker you wish to remove with a hair dryer set on high and held about 6 inches away from the fret board. Sweep the nozzle of the hair dryer slightly from side to side so that the heat does not become too intense on any part of the surface of the neck.
Try to pry up the marker after about five minutes, using the edge of a flat hobby knife. Work slowly and gently, being careful not to gouge the fretboard. Reapply heat occasionally if the glue resets and the marker becomes hard to lift.
Apply heat for another five minutes if the marker does not loosen, then try to pry it up again. If after 15 minutes of heating the marker still will not loosen, it probably was not glued with removable glue and should be removed by a professional.
Clean any remaining glue from the depression in the fingerboard with a bit of steel wool.
You can further protect your fingerboard from overheating by cutting a hole about the size of your markers in the centre of an old potholder. Place the hole over the marker before you begin to heat it; this will deflect heat away from the frets and the rest of the fingerboard.
Improper marker removal can permanently damage your fingerboard. Do not use excessive pressure when trying to remove the markers and be very careful not to damage the wood. If you're not sure of what you're doing, have the removal done by a trained professional. Excessive heating of the fingerboard can cause the glue holding it to the neck to soften. Do not attempt to heat the fingerboard marker for longer than 15 minutes. This technique will work with prefabricated acrylic inlays that were bonded with hide glue. "Poured-in-place" acrylic inlays have likely bonded with the wood and can not be removed without damaging the fretboard.