Q: BMW 2010 x3 fuel filter

Poor mileage has many very common causes other than dirty fuel injectors. However, if a diagnostic (that is, actual tests) suggests that fuel injectors are dirty the only way they can be cleaned is by removing them from the engine and sending to a lab such as Mr. Injector where each injector is cleaned ultrasonically on a machine, measured (for output volume, variation from injector to injector, and spray pattern) and the internal filter basket is removed from each injector and replaced with a new filter. Service short of that is frankly a waste of time and money but of course "on car" injector cleaning is a huge money maker. Again, if you want to clean and service a fuel injector, it has to be REMOVED from the engine and not only cleaned ultrasonically but then tested on a machine for volume and spray pattern once the cleaning is done and it needs a new filter (ALL that typically costs around $17 per injector by the way). That is the ONLY way injector "service" has maximal, or even "reasonable" value as a diagnostic for your particular issue which is suspected poor fuel economy. If clogged injectors were even a problem in your case, and it might not be, for all you know the filters in the injectors are still clogged simply because no amount of on car cleaning will ever dislodge particles or dirt that are captured in the incredibly fine filters that are used on injectors. The filters simply have to be replaced.

As noted at the outset of this answer though, of equal concern, there are a multitude of "as likely" causes for the poor fuel economy you are experiencing and, consequently, before money is spent on a speculative (and possibly useless) service such as on car injector cleaning, ALL of the following quite common faults should have been carefully ruled out: faulty oxygen sensors; inaccurate or defective coolant sensor; intake manifold or EGR valve leaks; faulty spark plugs, dirty engine air filter; faulty engine cooling thermostat, and so forth (there are quite a few others, too many to list here, that are checked before we suspect fuel injectors). If, at present, the vehicle has mileage (MPG) that is 10% or more below the EPA ratings, and you are driving as contemplated in the EPA ratings scheme (the percent distribution of city versus highway or city/highway alone), then I recommend you request a diagnostic for poor fuel economy. You need a diagnostic to determine the actual cause of the poor fuel economy; unless the injectors were SPECIFICALLY diagnosed and tested, the service was just offered as a "guess". If you have additional questions or concerns, by all means please re-contact us.