The Germans did in fact have tanks in World War I, they field about 20. I believe the only surviving example is in Australia if memory servies.
The French and Americans also used tanks in large numbers, with the Americans mostly using French tanks.
The British were actually -- despite the later Italian claim in Lybia -- the first to use tanks in the desert. I believe two or three tanks actually were used (without much luck) in Palestine. I've never been able to get a clear cut answer on how the tanks actually arrived there. It was discussed here:
http://1914-1918.invisionzone.com/forums/index.php?showtopic=48439&hl=tanks
Now back to the badge. I personally don't think it is real. Maybe others can comment. It is pure fantasy IMHO. I don't believe it is inter-war either. I have seen these called "Free Corp tank badges too." I don't know where hte Free Corps were getting armor from?
Here is a link to a reproduction WWI German tank badge:
http://www.militarytour.com/reproductions/WW1/12.htm
This is the correct design I believe.