Wicker Ottoman Help, My Ottoman Might Disintegrate?

Help, my ottoman might disintegrate? - wicker ottoman

I bought a sturdy wicker ottoman at Pier One a few months ago, has put a square on a cushion on top. Living in Washington, when it arrives. Then I saw this pile of "sawdust" kind of things in one place. So natural, cleaned and I was waiting to see. The next day there was a small pile. So ..... I think there is any creature, and I want to stop. Any suggestions would be appreciated really. Is there anything to stop spraying this event possible without destroying them my ottoman.