Allira
My MIL used to give me pieces of scrim, she worked in the towels and linens department of a big store. They lasted for years but I had to throw them out in the end.
Our window cleaner uses a brush attached to a water system with distilled water.
It's just the insides which spoil the effect, everything I've tried ends up with a smeary finish.
The best thing was tea with a non-fibre cloth but a lot of elbow grease was required.
Our window cleaner uses the same method as yours.
The first time he came, and I saw how wet he left the windows, I couldn't really believe that they could dry naturally without leaving marks, but they did. It still amazes me.