It's not a gasket. It (nylon) is there to reduce sqealing, with moderate effect btw. I see no objection to reuse it. I'd apply some Ate silicon grease, but not much. Buy genuine pads. They are best, asbestos free nowadays and they have the red line. Post a picture of the pads you have now and measure them. Some here may tell you by comparing them to theirs, how much they're worn.