Windows that 'appear' greasy are not actually greasy as such, they are just really grimy.
Grease itself of course is not water soluble so won't readily come off using just WFP.
BBQ grease is awful, it is almost similar to the inside of an oven door, not easy to get clean with trad let alone WFP!
If windows are really grimy, see if you can connect up to the householders water supply, wet the windows (regardless of what water you are using) and as fiddly as it may be, dip your brush into a bucket of diluted detergent (TFR is ideal of course) and wash windows and frames down with this.
I'm not sure, but I think I've heard that Tucker do an 'auto feed' system with their poles and brushes for detergent...could be wrong though...something like this would be ideal for those 'minging' jobs.
Maybe Gardiners will develop one!

Having washed frames and windows down with detergent, cleaning them up with pure water afterwards should be quite straight forward, just be sure to get rid of all suds!
Ian