I didn't even know the Z4 screenwash pump had a filter until this evening.
I could hear the pump operating, the jets seemed unobstructed, but the flow was more of a dribble.
Disconnect the wiring plug from the pump and the pump can be pulled straight up. It will probably bring the small filter with it, if not, just prise that out of the reservoir.
Once out give it a good clean, or renew it. The headlamp wash pump has a similar filter in place, so check it out.
It's a good time to thoroughly wash out the reservoir as well.
This is what the one on my car looked like -

I could hear the pump operating, the jets seemed unobstructed, but the flow was more of a dribble.
Disconnect the wiring plug from the pump and the pump can be pulled straight up. It will probably bring the small filter with it, if not, just prise that out of the reservoir.
Once out give it a good clean, or renew it. The headlamp wash pump has a similar filter in place, so check it out.
It's a good time to thoroughly wash out the reservoir as well.
This is what the one on my car looked like -
