i know a lady who works for a handbag manufacturer... she told me cheap hairspray (aquanet is the best) takes out ink marks out of leather!!!
she told me her daughter did a horrible job of drawing on a friend of hers couch and hairspray took it out!! test it on a spot first, like cheap leather or the straps!!! you can always spray some on a q tip and rub.... or try a regular white eraser!! it worked for me to remove stains from rubbing on my jacket!!!
she told me her daughter did a horrible job of drawing on a friend of hers couch and hairspray took it out!! test it on a spot first, like cheap leather or the straps!!! you can always spray some on a q tip and rub.... or try a regular white eraser!! it worked for me to remove stains from rubbing on my jacket!!!

I've never tried this on a handbag, but hairspray gets ink out of just about anything else. Good Luck!