Ahhh !! Mid century modern ?? Love that style because I lived through it !!
First step ,, If the paint can be felt as a raised area use a single edge razor blade and try to slide the blade between the paint and the wood !! It will leave a white area still but that may be able to be reduced with warm water and a bit of dish soap and an old toothbrush !! The toothbrush will conform to the grain in the wood !! May take several tries but do not let the area dry between each time !!
When using the razor blade just make sure you keep the blade flattened against the wood !! You just want to remove any thick paint!! The water and the toothbrush will lessen it even more !! When that is done and you have removed all the paint possible we will go to step two !! Just post back here when done and let me know the results !! Try to stay in the immediate area of the paint with the toothbrush !! Do not need to do more work than necessary !!
Today is a bit busy for me but this evening I will tell you what I would do if it were mine !! I restored many pieces with damage when I had my shop !! While it may be a bit involved as a step by step method it is really not difficult to do,, more a pain in the butt than anything !! I am kind of concerned about the paint that looks like its in the seam !!