this is a hard one.
I'm not sure a Mana Barrier would do anything in this particular case.
While I agree that mana barriers stop mana - and thus spells, Banishing is a skill, and not a spell after all...
Yet, the act of banishing can result in Drain, which is usually caused by the effort of manipulating mana...
Personally?
I wouldn't let a Mana Barrier affect a Banishing attempt, but this is just me, and I have no RAW/RAI to support that. And while I like magic and the magic system in SR (I usually play mages myself -and use Spirits), I also admit that spirits can/are a bit over powered, especially for some groups, so any player willing to try to Banish one as opposed to just trying to mana blast it, I'm not going to throw up any arbitrary additional modifiers. Especially at Fx2 hits (not net hits).