On my 2005 focus the lcd screens for the climate are looking like this. They are showing what they are supposed to, but in daytime it's annoying to look at a half peeled-off screen protector. 

 

Any way to re-sit it or remove it without damaging the screen?

While I’ve not worked on the mk2 climate panel, I’ve had the mk2.5 version apart a few times as I switched my internals to a different outer with black coloured buttons etc
 

If you pop the radio fascia off you should be able to unscrew the 2 screws holding the climate panel into the dash. 
 

Then release each of the electrical connectors by pushing catch in and lifting up locking arm which will disengage the connector. 
 

Once the panel is removed you’ll see around 6 clips spread around the module, gently release each of these and you’ll be able to pull the rear cover of the unit away from the front panel. 
 

Some clearer photos here

https://www.ebay.co.uk/itm/185831937058

Then the circuit board and displays will lift off the front panel leaving the buttons captive in it. Maybe keep the front panel face down in case the buttons are loose at all. Pretty sure the board isn’t fixed into the front panel but there should be a rubber membrane sitting on it for the interface between the buttons and their microswitches.

This should let you have a better look at the display screen etc. Reassembly is easy enough, just be cautious of getting any fingerprints on the LCD screen if it fits into a clear cover as part of the front panel. 
 

Can sort some more photos if you’re stuck as I’ve got a spare Mondeo unit to demonstrate with which is same design but very slightly different outer housing so couldn’t use the casing for my Focus. 
 

Have noticed the housing clips are different on mk2 version so edited post to correct that

4 hours ago, troy45 said:

While I’ve not worked on the mk2 climate panel, I’ve had the mk2.5 version apart a few times as I switched my internals to a different outer with black coloured buttons etc
 

If you pop the radio fascia off you should be able to unscrew the 2 screws holding the climate panel into the dash. 
 

Then release each of the electrical connectors by pushing catch in and lifting up locking arm which will disengage the connector. 
 

Once the panel is removed you’ll see around 6 clips spread around the module, gently release each of these and you’ll be able to pull the rear cover of the unit away from the front panel. 
 

Some clearer photos here

https://www.ebay.co.uk/itm/185831937058

Then the circuit board and displays will lift off the front panel leaving the buttons captive in it. Maybe keep the front panel face down in case the buttons are loose at all. Pretty sure the board isn’t fixed into the front panel but there should be a rubber membrane sitting on it for the interface between the buttons and their microswitches.

This should let you have a better look at the display screen etc. Reassembly is easy enough, just be cautious of getting any fingerprints on the LCD screen if it fits into a clear cover as part of the front panel. 
 

Can sort some more photos if you’re stuck as I’ve got a spare Mondeo unit to demonstrate with which is same design but very slightly different outer housing so couldn’t use the casing for my Focus. 
 

Have noticed the housing clips are different on mk2 version so edited post to correct that

Sounds like a mini project. I'll see if I can try to do this when I get some free time.

Thanks for the detailed explanation!