You did write that you know but butterflies has nothing to do with this. Бабочка is butterfly and babushka is бабушка. Babushka lady was most probably first time used by some of the researchers or reporters.
The original early plot called for blaming the assassination on the Communists and Russians.... They wanted to make it appear that he mystery woman was a Russian.....Thus they dubbed her Babushka.... In Texas a more appropriate moniker would have been "Bandanna Lady" if it had been a spontaneous and un-contrived label.
You may recall that the early reports said that Lee Harvey Oswald was the leader of a band of communists under the banner of the Fair Play for Cuba Committee .....