There *wasn't* any group of "professional archaeologists" at the time. Schliemann was a pioneer. Sure he was destructive of the layers of Troy, but simply out of ignorance, not a vandal and looter like Belzoni.
You had various scholars who collected antiquities and attempted to categorize and catalog them. But the actual organized methodology of excavation . . . with strata and grids and all the rest . . . didn't catch on until a decade after Schliemann. I think Rivers and Petrie and Evans were the first that you could really call professionals.
But the material he discovered was amazing (the "Treasure of Priam" finally turned up after the Russians admitted they looted it from the Berlin Museum).
Of course, this is all based on my reading in my Art and Archaeology and Classics courses, we're talking about 50 years ago now!