I agree that 'her' could be omitted in this sentence depending on what she was doing. If she was killing bears or husbands then 'her' would be used but in this case it could mean she had nothing on her hands such as gloves. I am a native English English speaker.
I agree, i dont think 'her' needs to be there. I dont know why they dont just use the literal translation when it makes sense. Yes with 'her' is more common in english but thats not what it says in the czech phrase.
If you omit it, you'd be understood but you'd sound like a foreigner. It is standard English to include the possessive here; it's not a matter of logic.
I'm native AmE, and while I agree that the possessive is usually used in English, I'm also inclined to agree with those who feel that it is not absolutely necessary in all cases.
As an example -- A: "How did you do it?" B: "I did it with my bare hands!" A: "You didn't even wear gloves?!?" B: "Nope, did it with bare hands."
I feel that the use of the possessive is, to some extent at least, context dependent. But since the possessive is often omitted in Czech, there could be a reason, which a Czech native may explain, why it would not be appropriate to omit it here. But if it would be okay to omit it, I will add translations that do not use it.