It's bridging and it serves to brace the floor joist.

By bracing the floor joist, you reduce the effective length of the joist and thus increasing the moment of resistance of the floor joist.

When designing any floor beam, you calculate the factored moment of both dead and live load combined.

You also calculate the unfactored live load deflection.

Factored moment must be less than moment of resistance and live load deflection must be less than length / 360.

If you remove the bridging, you are removing the bracing which increases the effective length and you will reduce the moment of resistance and the beam could fail.

So bottom line, do not remove the bridging.

Note, I read other posters stating that at this point of time it will not matter. That is wrong. It definitely matters. Other posters think the bridging serves to transfer load to the adjacent joists. That is also wrong. It's a brace. It works by preventing the joist or beam from twisting under load and thus failing.

Cheers.