If there's a big change in the rate, it's a good bet that the old mainspring is set and should be replaced. If the rate remains constant, there's nothing wrong with the mainspring and the clock can be regulated. The British Horological Institute only really condones removing a mainspring using a proper tool. However there are many repairers who remove a mainspring by hand. If you do remove a mainspring by hand, you must be aware of the following precautions.
ALL times is safety.
Wrap the barrel in a thick cloth. Take care not to distort the spring. Use the lathe - any lathe will do, as long as it has a toolpost, a cross slide and a lock on the headstock mandrel to stop it turning. Make a centre spindle to hold in the lathe chuck with a hook to hold the inner end of the spring, just like a regular winder. Fix another hook in the toolpost to hold the outer end of the spring.