If you want it gone without pulling the wood, activated carbon in the filter is the direct answer and it works fast — usually visibly clearer within a day or two.
Things to know so it does not become a permanent fixture:
It exhausts. Carbon binds until its surface is full and then it is just an expensive sponge. A month is a reasonable working life; after that it does nothing and people leave it in for a year believing it is still working.
It is not selective. It pulls out tannins and it will also pull out liquid fertiliser and anything else dissolved. In a planted tank that matters — if you dose ferts, dose after the carbon has been in a while or you are partly feeding the filter. Some people run it only for a week to clear things up and then take it out, which for your situation is what I would do.
Purigen is the alternative people reach for. It targets organics, it is more selective, and it can be regenerated rather than replaced. More expensive up front, cheaper over a couple of years, and it goes visibly brown so you can see when it is spent, which is genuinely useful.
Either way, the wood keeps leaching underneath. You are treating the symptom, which is fine, but expect to repeat it a few times before the wood settles down.