Agree it’s most likely an action/bedding or recoil lug problem. Have you checked the action screws for torque ? Get hold of a torque wrench and check what pressure they’ve been tightened to. If they are loose that could be the problem. Be careful not to over tighten as this can bugger up the free floating recoil lug set up which is critical to the design of T3s. From memory torque should 30 or 35 in/lbs max for Tikka factory stocks. I’m assuming it’s a factory Tikka stock ? Is it ? If it’s an after market stock with ali bedding block then that can present other issues.
Take the action out of the stock and carefully inspect the stock internals where the action sits for signs of rubbing and also check the bottom of action looking for rub marks. This will confirm that you’ve got a bedding or seating issue. When you’ve got it apart check there’s no shite to grit trapped anywhere, especially in recoil lug area and recess.
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