Will this sieve ruin my carbonation?

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.