Most of the musical influences were indirect. If you look at something like Alois Fleischmann's "Sources of Irish Traditional Music" you'll find a great many Scottish tunes that passed into Irish tradition (far more than the other way).

BUT they were Gaelic and Scots indiscriminately. Many of them were transmitted on paper, since Scottish music publishing became an enormous force after 1750, and itinerant musicians were never many links removed from somebody who could read a copy of Bremner, Daniel Dow, Aird etc. And those anthologists didn't usually separate out their tunes by regional origin (if they even knew it). There would have been no reason for a practicing fiddler to pick out just the "Erse" numbers from a tunebook when visiting Ireland - if a Scots or English tune was interesting they'd surely play it.

There was no distinctive channel that communicated significant amounts of music from Scottish Gaels to Irish Gaels *alone* without involving other cultures. (There must have been some sharing of songs between fishing communities on both sides of the Irish Sea, but it would take detailed linguistic analysis to work out the direction for any one of them).