besmirch (someone or something) with (something)
To tarnish one's or something's reputation in some way. Don't besmirch my stellar reputation with those lies! A few disgruntled patrons have besmirched the restaurant's reputation with their negative online reviews.
besmirch someone or something with something
to dirty or soil someone or someone's reputation with something. Please don't continue to besmirch Alice with that gossip. You have besmirched my reputation with your comments. He besmirched her with vile gossip in order to turn people against her.