It could (most probably ) be your pilot bearing or your throw-out bearing.... always replace both of them at the same time...while you are up in there...and I would never leave the old clutch in there and put it back together either..... those three things are almost always replaced together....
I had an oilite pilot bushing that actually Screeched.... in a 1968 6 cyl Chev.... but I put in a bearing as a replacement...
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