I put the screw back into the handle through the black tube and secured it, but it won't seat. It seems like it sits too high.

More details please. Brand and type of faucet? What's it on? Are the threads too big for the screw so it can't be tightened? Is this a screw on top under a pop off cap or a Allen Set Screw in t5he base of the handle? Back to you, Tom

Take a good, clear picture of it and post it for us to see. Back to you. Milo