Actually, a lot of them came with that H stamp. At that time, at flee markets, terms Novodel and Fake/Replica were completely interchangeable. Fakes were routinely called Novodels, and no one meant it as a reference to the 18th/19th century mint struck Novodels. It was just a polite way of referring to a coin that is not genuine. I think that left a bad taste in Russia for actual Novodel coins.
BTW, I assume you know that the officially struck novodels did not have any such counterstamps.