Rav Moshe and shaking hands

Question

"In 1971, I asked Rav Yisroel Belski to ask Rav Moshe Feinstein about this because I had a woman boss. Rav Belski wrote to me that Rav Moshe said tarud b'melachto and therefore mutar." Look at Igros Moshe Orach Chaim 1 siman 113, Even Haezer 1 siman 56, and Even Haezer 4 siman 32 paragraph 9. Rav Moshe clearly did not hold it was mutar.