When only the color layer is missing, you may be able to fill the bottom layer of paper with matching color; otherwise, remove base paper from the wood using a razor blade and continue with the following steps.
With X-acto knife or razor blade, trim edge of torn area to get a straight line.
Scrape off any glue remaining on platform with razor blade.
Select paper which best matches thickness of puzzle paper and cut a piece slightly larger than missing section.
Dab spot of Elmers Glue-All on bare area of puzzle piece, abutt paper edges of new and old paper and press with weights or clamps overnight.
With piece upside down on a disposable wood surface, with X-acto knife cut off excess paper around knob or puzzle piece. File edges of new paper smooth to match wood underneath.
Use water color pencils as in coloring a replacement piece above but try to use only dry or damp pencils as most areas missing paper are small and need only spot touchup.