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If it's smooth glass I would use a scraper to cut it off the glass and remove and last bits of residue with a wipe (alcohol or wonder wipes). The scrapers of this style are my preference :-
As others have said, you need to be careful and cut between paint and tape to retain the edge of the paint. If it's exterior and properly taped it should have a 1 - 2mm gap between the woodwork and tape which is painted as this helps the paint to protect the woodwork.
I don't carry or use a hairdrier in my tools so I can't say if that works better.
I use a lot of masking tape on some jobs. Some clients don't mind or notice the details though. Very often I'll fuss over one of my own rooms and never notice the details again!