I see both your points (oops). While the fence (which surrounds our neighbor's backyard) is an aesthetic interruption, it aids in storytelling. I'll encourage "Bucky" to pose in another location in the future.
Our yard is somewhat of a funnel because both our neighbors have fences and there is a natural area nearby. This deer was limping when I saw it. I wonder whether the dark area on its left rear leg is a sign of vehicle impact.
I will disagree with Mr T. I think the fence helps define the story - an urban deer.
But the photo could possibly be reworked more to darken the background just a bit to emphasize the deer.
The is almost as good at the preeminent DaveV, absent now, but National Geographic good at these kind of shots...I am not saying you should not have taken this, (it really is a fine shot), but the fence spoils it a little for me...maybe shoot from a 2nd story window, down, and so most if not all of fence can be cropped out?
There have got to be ways to shoot this again, and again this winter...with patience, (however I had a 2nd change at pool balls this evening w/o time pressure, etc....and they were all terrible....go figure....hummm?) Best Wishes, Traveller