Oak has a very open grain. Sometimes the deep pores can be seen like a super fine honey comb. Paint that gets deep into the pores may not be removeable without scraping down the wood. Get it minimal and use a loupe to look at what is left imbedded. The best you might be able to do is reduce it to acceptance. A shop nightmare is using a green pencil eraser on Oak. The green particles get into that open grain and really stand out, impossible to completely remove without scraping down.
About that open grain on oak. Some of the softer hand applied finishes, TUNG oil in particular, can run through the open grain and out the other side of the board! Saturation like this can cause the wood to bleed out for years. I tend to use a finish that has a distinct drying characteristic instead of an aging characteristic.