I agree. A complete fake. There are a lot of cast fakes turning up on eBay these days.
For such a relatively common badge, originals are extremely well-made. If you look at page 2 and 3 of the link given by JapanX, I give a fairly comprehensive survey of the variations of this badge. There are at least 7 variations with slightly different details in the central medallion, finish, pin/hinge construction and inscription on the back.
While the most common one with silver finish over copper/bronze with a square flat pin marked Hamburg 11 goes for only 50 or 60 Euros, the more deluxe ones with gun-blue oxidized finish, more detailed storm trooper, coke bottle, U-shaped, or brooch pin and marked Hamburg 3 and the even scarcer Ges. Gesch. can go for over 100 Euros in mint condition.
I recently sold the mint Hamburg 3 in a scarce Hamburg 3 box illustrated on page 3 of the above link for 200 Euros.