The phrase "soft pedal" means to lessen or reduce something, like sound, force, or intensity. It is often used in music to describe making a piano sound quieter by pressing a specific pedal. Full definition
I hope manager Roy Hudgson will soft pedal on playing Welbeck in his 2 friendly games as Arsenal can not afford any injury happening to their inform striker Walcott at this crucial title run - in stage in the season. (justarsenal.com)
HP subsequently started soft pedaling that notion, and last week threw in the towel on the public cloud business, refocusing (again) on helping customers use Amazon or Microsoft (MSFT) Azure to backstop their HP private clouds. (fortune.com)