Free delivery direct from ALThe edge of the removal tool needs to go into the push fit pipe coupler to the left (in the red box following the arrow), the grab ring that holds the pipe is in that coupling tee as they call it. You'll need 2 probably as both will need to be disconnected to pull the unit forward. The white plastic pipe to the right on the back of the shower body, that the pipe is running through, is just a guide/jig for the pipework coming in from the wall behind.
View attachment 361053
They're wrong and I am surprised, AL are usually really good with their support, as you say though the unit is 20+ years old.
The tee coupler you are trying to get disconnected looks to be this one
https://www.showerspares.com/search/rear_entry_tee_piece_129601/ with other bits too https://www.showerspares.com/aquali...all/aqualisa_aquastream_1997-2003_aquastream/
and this is the spares catalogue, so other bits may be available too
Aquastream Rear Entry Tee (97-03)
Rear entry tee suitable for Aquastream power shower models between 1997 and 2003.
www.aqualisa.co.uk