Scrape off the old tape and put some automotive grade 3M double sided tape they sell at any auto parts store. Make sure the badge and the fender are free from old tape residue and clean off with some alcohol. That should work.
I reused one of mine. But I came across some special adhesive that worked fantastic. It has a backing, but not plastic film - it is adhesive only. You simply press the "tape" against the badge backside, then when you peel off the backing, only the adhesive remains. Couldn't be easier. Super sticky and virtually no thickness at all.
Unfortunately I have been having trouble sourcing it.