If it has an ear tag, it is considered someone's livestock. 'Pretty sure it is illegal to deliberately kill it. Your decisions as to who tells;brags/announces what, what happens to the ear tag immediately after the kill, etc. is your business.

If it has an ear tag or someone reports it missing, what's the process to get the animal back to its owner?

Sec. 142.003. DISCOVERY OF ESTRAY; NOTICE. (a) If an estray, without being herded with other livestock, roams about the property of a person without that person's permission or roams about public property, the owner of the private property or the custodian of the public property, as applicable, shall, as soon as reasonably possible, report the presence of the estray to the sheriff of the county in which the estray is discovered. (b) After receiving a report under Subsection (a) of this section that an estray has been discovered on private property, the sheriff or the sheriff's designee shall notify the owner, if known, that the estray's location has been reported. (c) After receiving a report under Subsection (a) that an estray has been discovered on public property, the sheriff or the sheriff's designee shall notify the owner, if known, that the estray's location has been reported, except that if the sheriff or the sheriff's designee determines that the estray is dangerous to the public, the sheriff or the sheriff's designee may immediately impound the estray without notifying the owner. (d) If the owner does not immediately remove the estray: (1) the sheriff or the sheriff's designee may proceed with the impoundment process prescribed by Section 142.009; or (2) if a perilous condition exists, the sheriff or the sheriff's designee may proceed with disposition of the estray under Section 142.015.

Call local sheriffs office ask if anyone has reported it missing in your area. He will tell you. Your good to go if no one has reported it missing you can also check with the local game warden to see if he has been contacted. I would do those two things before heading to the woods again because the temptation will be to great if he shows up.

100% don't shoot an animal with a tag -- even a legal game animal,

White tailed deer during season, ear tag or not, are fair game and can be taken, assuming you are hunting on owned or leased land. That’s also assuming it’s a legal deer and your not on the originating property where the deer came from and covered by a contract.

If you see an ear tagged amazing white-tailed buck on owned, leased or public land can you legally kill and claim it during season?

Can anyone provide documentation saying you cannot?

I can positively identify this as backstrap, tenderloin, neck roast, cube-steak, and ground meat....and a rack for the wall. Good luck getting him!