climb down vs walk back

climb down

• Used other than figuratively or idiomatically: see climb, down. 

• To abandon, withdraw from, or soften a previously expressed opinion, argument, etc. 

• An abandonment, withdrawal from, or softening of a previously expressed opinion, policy, argument, etc. 

walk back

• Used other than figuratively or idiomatically: see walk, back. 

• To withdraw or backpedal on a statement or promise.