That is an interesting problem. Bananas have to deal with wind damage, sometimes they get very shredded up yours seem to have just gotten broken. Maybe the corner of the house is subject to some wind rotation? If so I'm not sure what you could do about it in an otherwise unsheltered location. Bananas are just susceptible to wind damage, in open areas they get very tattered in anything over 40 mph winds and can get completely ragged. Those broken branches will dry up and can be cut off. Bananas have a root system which likes to extend as much as six feet out from the corm, but your grass is taking up that space. It will benefit from mulch, fertility, and root space to grow.