The SMMA should have a contract where there’s mutual indemnification so if the influencer posts and the brands sues technically the influencer is on the hook to indemnify the SMMA. Generally, there’s a professional clause in a proper contract with an influencer and take down clause if the professional clause is violated.
We informed the brand immediately who we had a good relationship with and then had our lawyer write a letter to the influencer.
I’ve had this happen where an influencer posted for. brand and then went on a rant about something else. The brand publicly disavowed any their connection with the influencer and influencer called out the brand. We sent her manager a stern letter from our lawyer that they were in violation of their contract and we would sue for damages. The posts were taken immediately.
Generally no one wants to sue or be sued. It’s fucking headache and costs tens of thousands of dollars. Influencers can do stupid shit but generally the threat of a lawsuit gets them to remove the content.