DMCA take down requests are an effective way to get your post taken down
If they post a copy of your picture, you own the copyright on that picture. DMCA has a notice and takedown approach. Facebook avoids liability if they take down any copyright request. If they leave it up, they are risking copyright liability and risk losing their section 230 safe harbor protections. If the first DMCA take down doesn't work, just try again until it does. Eventually you will get someone who will just take it down.
I don't know if it would work for text only posts, nor am I endorsing this, but one of the main criticisms is that it has the chilling effect of silencing speech because the penalties for making false reports is pretty low/non-existent. Most companies just take down anything rather than take on the risk of liability.