I think as long as the season includes white-tailed deer and you are legally licensed you'd be "legal". Just hide the rope lead before you tag it and I'd be prepared for some fallout from the owner of the managed property. Are you planning to have the mount done with the ear tag in place or with the big hole it leaves behind? It would help your cause too in that managed property was three or four parcels away from your property too. If you are right next door you should be certain that you can prove the deer was out of its own accord.
If I lived adjacent to a deer farm and saw what I knew was a deer that came from that farm out of the enclosure I'd call the owner. The brewha that shooting said deer could stir up wouldn't be worth killing it and you might end up with more headaches than the deer is worth. But that's just me.