> 費用の１０％の手数料を引いた金額をお返しいたします

Does this mean they will return back 90% of the money or only 10%?

The answer is they will return 90% but could you explain me how to translate
this sentence from Japanese to English so it will makes sense to me?
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Why does this mean they'll return 90% of the money, not 10%?
The answer is that they will return 90% of the amount you paid.

* * *

The key is breaking the sentence into parts correctly. Given:

> 費用の１０％の手数料を引いた金額をお返しいたします

The main verb in the sentence is お返しいたします. This is a polite humble
construction. いたします = します in humble form (謙譲語) and the construction お返し +
いたします construction makes it really humble. All of this means 返す if we strip
away the layers of politeness.

Now we have

> 費用の１０％の手数料を引いた金額を返す

the object of 返す is ~~~金額 (marked by the を)

So

> 金額を返す = we will return an amount of money

But to know what amount of money, we have to look at the verbal construction
modifying 金額. In Japanese, a verb can be used to modify a noun so the part in
front is a construction that modifies the noun.

the verb there is 引く which means to withdraw or subtract in this context.

費用の１０％の手数料 = a ten percent usage fee and this is the object that has been
subtracted.

* * *

Reworded into English,

> "We/I will refund you the amount you paid minus a 10% usage fee"
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The clause "費用 (expense) の１０％の手数料 (10% commission) を引いた (subtract)" modifies
the noun _amount_ (金額). It works like a relative clause in English. It can
literally translate to

> A 10% commission of the expense is subtracted from the expense.

The translation of the full sentence is

> We will return you the amount after 10% commission of the expense is
> subtracted.
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