The link to the 4 minute video in post #7 above also gives the sizes for the bits needed to remove the 3 screws securing the handle to the door...in case one chooses to replace it vs cleaning as as also suggested.
BTW...this thread revealed to me what I had not observed before...the e70's driver's door handle is designed completely different than the passenger's doors. I never noticed that it didn't have the curved pull handle (#15 & #14 in the diagram). How did I not notice that blaring difference?