Go into the DEVONthink preferences in the Settings app and select Reset at Start-Up. All of your databases will be deleted from DEVONthink To Go and you’ll need to re-sync to get the others back on your iPad.
I tried that and it didn’t work. So I completely shut down DTTG on the iPod and on my Mac. re started it on both machines, did a sync again and then tried it and it worked. I was able to get a delete button and the database got deleted from my iPod.
Not sure why I couldn’t get the delete initially as that was what I was expecting to happen.