Longshanks, good evening.
I must admit I can not ever seen such a handle?
Going by form, the inner [rusted] cap will probably conceal a nut or screw which passes through the screen and attaches to the handle proper.
As for how to remove the rusted cap? how about using a pair of "Footprints" or a shaped pair of "mole Grips"
BUT? there is generally a "But"
If you do attempt this method, use plenty of soft protection around the Cap cloths Etc. using short up and down movements may release the cap enough to then remove by hand.
Next "But" is that you will probably destroy the cap in trying to get it of ? these caps [ it it is anything like one of my Radiators ] are a push type fit.
Only suggestion I can come up with is that once you have removed the rusted cap, try to locate a replacement? or a near fit + Mastic??
WD40 may assist in the removal process??
Is there a makers name anywhere on the screen? if so revert to Google?
Problem with Bathroom White goods is that the manufacturer produces [say] 5000. And as the saying goes, when it is gone it is gone, also these units after a short production run are considered obsolete by the Manufacturers and Retail outlets. Such is the way of this sort of unit.
Ken.