"...is subject to a court order that restrains such person from harassing, stalking, or threatening an intimate partner of such person or child of such intimate partner or person, or engaging in other conduct that would place an intimate partner in reasonable fear of bodily injury... "
A mutual restraining order as used by Georgia courts does none of the things set out in the federal definition you set out, and therefore the so called restraining order does not create the prohibition on gun ownership or possession created by the federal statute.
You also omitted subsections (A) and (B) of the statute you quoted, which are key to its implementation:
(A)was issued after a hearing of which such person received actual notice, and at which such person had the opportunity to participate; and
(B)(i)includes a finding that such person represents a credible threat to the physical safety of such intimate partner or child; or
(ii)by its terms explicitly prohibits the use, attempted use, or threatened use of physical force against such intimate partner or child that would reasonably be expected to cause bodily injury; or
Neither of these conditions precedent are established in a Georgia mutual restraining order, both of which conditions are necessary for the Lautenberg Amendment to kick in.