brush down

Short definition from Wiktionary

Verb

1. 1
   Used other than figuratively or idiomatically: see brush, down. To remove something with a brush, or ones hands using a downward brushing motion.
2. 2
   To straighten up one's clothes and to tidy up one's appearance.

Noun

1. 1
   The act of brushing down (a person, animal or object).