I don't know where you got that, but it doesn't apply to this law HR2640, note that in what you did post, the remedy can be obtained through a fed court. Relief from the disability must come from state action here, because that's where the action originated. The appropriate section of the new law type HR2640 in search is:
SEC. 105. RELIEF FROM DISABILITIES PROGRAM REQUIRED AS CONDITION FOR PARTICIPATION IN GRANT PROGRAMS.
(a) Program Described- A relief from disabilities program is implemented by a State in accordance with this section if the program--
(1) permits a person who, pursuant to State law, has been adjudicated as described in subsection (g)(4) of section 922 of title 18, United States Code, or has been committed to a mental institution, to apply to the State for relief from the disabilities imposed by subsections (d)(4) and (g)(4) of such section by reason of the adjudication or commitment;
(2) provides that a State court, board, commission, or other lawful authority shall grant the relief, pursuant to State law and in accordance with the principles of due process, if the circumstances regarding the disabilities referred to in paragraph (1), and the person's record and reputation, are such that the person will not be likely to act in a manner dangerous to public safety and that the granting of the relief would not be contrary to the public interest; and
(3) permits a person whose application for the relief is denied to file a petition with the State court of appropriate jurisdiction for a de novo judicial review of the denial.
(b) Authority To Provide Relief From Certain Disabilities With Respect to Firearms- If, under a State relief from disabilities program implemented in accordance with this section, an application for relief referred to in subsection (a)(1) of this section is granted with respect to an adjudication or a commitment to a mental institution or based upon a removal of a record under section 102(c)(1)(B), the adjudication or commitment, as the case may be, is deemed not to have occurred for purposes of subsections (d)(4) and (g)(4) of section 922 of title 18, United States Code.
The Supreme Court, IIRC, has already ruled that failure to act on such an application is not a denial.
BTW, the information is in the original article by "Pro Gun New Hampshire", which was defending HR 2640 and the NRA.