The inquiry follows a New York Times report that aides to Mary Peltola helped recruit an outside candidate with a name similar to that of her Republican rival.
The Vietnam Veterans of America, Veterans for America First and other groups are set to join a brief in favor of the arch, which would be built near Arlington National Cemetery.
The race between Ken Paxton (R) and James Talarico (D) has revolved around the issue of government corruption, a top voter concern just behind the economy.