One of my friends, being part of XLRI Jamshedpur, has a better insight on the same. Here is what he has to say about the selection procedure at XLRI.
For interviews, XLRI shortlists students based on their XAT percentile. But once you get a call for the interview, what will matter more is your personality, and profile rather than your marks.
My friend got an interview call for his Satellite Business Management course (PGCBM) in XLRI, Jamshedpur. During his interview, the professors commented on his poor B.Sc marks. But they also put emphasis on the quality of his overall General Knowledge (GK), Subject Knowledge of Statistics, Supply Chain, and Operation Research.
So, to answer your question, marks do matter to some extent, but if you have an impressive profile you can do well in the interview.