The speakman kent handles are sometimes very hard to remove. A handle pulle is the only way to get the old handles off. The second problem is removing the escutcheon tubes. The tubes unscre off the body of the faucet and like the handles they can be a bear to get off. Spray some WD-40 or liquid wrench inside the tube and let it sit for a while then put a rag around the tube and try to remove it with a pair of pliers or a strap wrenh would be even better. If you damage the tubes don’t panic they are available for replacement as well as the handles. I will put a link to the parts breakdown of the speakman kent faucet it should help.