My (mechanical) Honeywell also has a single screw. It's on top right hand side and doesn't need to be fully removed ; just unscrew it enough for the head to be clear of the cover. The cover then slips off ( pull from the right hand side first , then disengage at a LHS lug)
I dropped dust into mine whilst repairing damaged plaster above it . The dust/ grit got into the moving parts of the thermostat. It no longer 'clicked' . I think I just blew the dust away. Normal operation was restored
Of course you could also have the added problem of cables being drilled through ..........
(Take the precautions mentioned above ) Ian