Sometimes to make things more English, you have to add things that aren’t in the original German text.

How about Eilanfragen an den Technischen Kundendienst richten. That is pretty typical and you could translate that as “Please address urgent enquiries to the technical customer service department.” A genuine Englishman (fee, fo fi fum, I smell the blood of ...) would however say “Please address urgent enquiries to our technical customer service department.”

It’s the same with fingers and thumbs and other bits of your body. When I complained to my German wife that she says das Haar instead of mein Haar, she just replies well of course it’s my hair, whose else would it be?

Maybe it has to do with the big Du/Sie question? Is the person you are writing to a mate or not? Fortunately everyone is a mate in English, so there is no dithering associated with a choice.

Anyway, I have learned my lesson and I try to sprinkle possessive pronouns liberally about, despite the fact that they are used much less frequently in German.