I'm from that area too and when I was growing up there, I don't remember anyone even mentioning the grave site, although they did talk about the "home" that used to be there.
But even in the 1980s, care conditions and standards were appalling. I remember visiting an old folk's home outside Tuam in the mid-eighties and the elderly people there were accommodated in disused stables. We were horrified.
Even in those times, there was a huge stigma associated with unmarried mothers. And god help any poor girl who had to "take the boat". My mother used to befriend unmarried mothers and have them around for tea because she felt people treated them like outcasts, and she was right, they were treated as outcasts. People were terribly mean-spirited and backward.
The Tuam babies story is in the news because a local historian did all the work of identifying death certs and accounting for where the remains were, and they only place the dead children seemed to have been buried was in this field, covered over with a concrete slab. A proper excavation of the remains is the first step needed, I think. And then a memorial accompanied by lots more research, so that the true story of the children of Tuam's "home" can be told.