1. To remove with a brush.
2. To snub someone

A curt or disdainful rejection.
When you give people the brush-off, you ignore them or refuse to listen to them because you are not interested in or do not like what they are saying.

1. When you brush people off, you ignore them or refuse to listen to them because you are not interested in or do not like what they are saying.
2. When you brush off a critical remark or problem, you ignore it and continue as before without letting it affect you.