Scrape some of it off and see if it dissolves in meths, in which case it is probably shellac..
Easy to remove using fine grades of steel wool soaked in meths.
If you keep a secondary bowl of meths to dip the steel wool into it will clean some of the finish out of it and help prolong its life, but you're still going to use a shed load of it.
If not and depending on their age, you might find it's been finished in possibly a 2 pack spray lacquer, in which case you're only going to get that off using acetone.
The best way I found was to lay a towel** on the area you want to strip, soak that in acetone, then cover that with plastic sheeting so the acetone doesnt evaporate and actually get to work softening the lacquer.
Once softened its going to be a cabinet scraper or stanley blade job, but you're going to lose the patina.
** if you're married, you can find an entire cupboard full of ideal towels that your wife has thoughtfully put aside for just this type of job..
