How do I rinse my filter and not loose my good bacteria?

Might be a dumb question but I’ve have my tank running since November and it’s doing great but the filter is clogged. I’ve rinsed it in tank water but it’s still leaching particles into the tank. I don’t want to straight up replace it and get rid of all the good bacteria I’ve grown but I’m not sure how to go about this lol I’ve only kept saltwater tanks before and had a sump that did the filtration and that made sense to me but for some reason I’m not sure what to do here and there seems to be differing answers on it. It’s just a simple filter hanging in the back of the tank with a filter that slides out with carbon in it