Will this sieve ruin my carbonation?

If your kombucha has very little carbonation, I would say this would almost completely remove the carbonation entirely. So it depends how much carbonation you currently have. As others have mentioned, running kombucha through sieves and filters does reduce carbonation, the type of sieve does make a difference, and the sieve you have in your picture seems like a mesh one, which does reduce carbonation by a lot.