Repairing Double Hung Sash Cords

Removing and Cleaning Pulleys

Here I've tried to separate the paint from around the housing of the pulley and around the two straight edge screws that fasten the pulley to the window.  Due to  the many layers of paint (looks like 4 of them) the screws just won't move without some additional persuasion.
a heat gun can soften the paint around the screws - you don't want to over heat the paint here - both because you don't want to vaporize any lead paint and also because it actually makes other parts of the pain adhere even more closely when it cools down. Just 5 or 10 seconds per screw. Multiple times if necessary.

You could also use a chemical remover - again more time, more tools, additional type of cleanup - but removes the risk of vaporized lead paint.
screws removed, paint edged with a straight end around the pulleys, genty pry off the pulley

 

here are both pulleys removed, hang on to the screws. They look terrible and we're going to fix that up.
clean the pulleys by immersing them in a TSP and boiling water mixture. Don't be shy with the TSP.

 

i use a small jar, 3 or 4 inches of TSP - put the lid on loosely (we don't want the cooling water to create a vapor lock but we do want to retain heat), and leave for 10 or 15 minutes (or longer if many layers). Leave alone  and almost all the paint will have fallen away. Scrape the rest off with a plastic bristle tooth brush or tile brush. We don't want to damage the finish of the pulleys with a metal brush.