Is there a danger of disturbing the paint surface if you take the badges off?
Hi, there shouldn't be. You would probably be best using a clay bar to get rid of the dirt around the badges properly.
you should be able to use a heat gun/hair dryer and some dental floss to bring the badges off the car. Most of the glue should come off it if not all.
Have done this process on my Caddy 2 months ago and came up great! and those badges had been on since 2008.
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Hair dryer and credit card worked for me, then a bit of elbow grease with wd40 followed by a polish and alls good on the jetta's rear.