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.

I believe that any time you pour a carbonated beverage between containers, you lose some of the carbonation because CO2 escapes. Pouring a carbonated beverage through a regular sieve causes CO2 to escape even more, and pouring it through a mesh sieve (at least it looks like a mesh sieve in the picture) will cause even more loss of carbonation.

So I would say yes, you are losing carbonation by using that sieve. If it's to filter out the fruits and what ever is in the kombucha, I would just do my best to have larger chunks that would fit through a regular wide holed sieve.

Yep! You know the old saying!