Congruences modulo powers of 2 for restricted partition triples due to Lin and Wang

In 2018, Lin and Wang introduced two restricted partition triples, whose generating functions are related to the reciprocals of Ramanujan-Gordon identities. Let RG(2)(n) denote the number of partitions triples of n, where odd parts in the first two components are distinct and the last component only contains even parts. Lin and Wang proved some congruences modulo 5 and 7 satisfied by RG(2)(n). They further asked the existence of the infinite families of congruences modulo high powers of 2 for the function RG(2)(n). Utilizing some q-techniques, we prove that such congruence families indeed exist.