Looks like the beginnings of hair/thread algae... you can try to physically remove it by using a toothbrush and brushing/twirling it away from the moss and wood. Spot treatment with H202 or Excel can also work, but the moss might also melt in the process.
Algae eating shrimps can help to consume it and clean up the wood and moss. If the tank is cycled, you could try adding amano/yamato shrimps, or even cherry or malayan shrimps (though you'll need more of those to be effective, as they are generally smaller in size and appetite). Don't feed the shrimps at the beginning, let them do their jobs and consume the algae first.
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