SHOP AROUND or get friendly with the service manager.
I agree !.
Some dealers are seeing this as an opportunity to over change there customers for the work, just because it’s a GTE.
Special car, special prices !.
I would ask to see the service manager and ask him to explain what the actual difference is between a cam belt replacement on a standard 1.4 TSI engine and a standard 1.4 TSI found in the GTE and then justify the massive difference in price, before you take your business to another dealership for life !.
Before he offers his opinion on the subject ( which he is unlikely not to have that knowledge ) remind him that the GTE does not have a mechanical belt driven water pump either O.B.T.W. therefore this should in fact reduce the costs of the repair.
Oh ....... While on that subject, go to the parts department FIRST and price up the cam belt and any other parts to carry out the belt change or BOTH models.
Just so you have the facts in front of you.
The service manager will either try and bull shit his way out of an embarrassing situation or he will say there has been a mistake and offer the work at the original price !.
It which case you either accept his offering or tell him to stick his offer where the sun does not shine, because his staff tried to rip you off and failed badly !.
Vote with your feet, your money is better spent at a dealer who is more trustworthy and honest ( if there is such a thing ).
Good luck in the search, it may take a while.