I have a question regarding this OG13 SC question:

As the cost of wireless service has steadily dropped over the last year and as mobile phones have become increasingly common, many people are finding that they can avoid toll charges on their home phones, using their mobile phones for making long-distance calls at night or on weekends, at a time which many wireless companies provide unlimited airtime for a small monthly fee
a) same as above
b) phones, instead using mobile phones to make long-distance calls during the night of weekends, during which
c) phones by using their mobile phones to make long-distance calls at night or on weekends, when
d) phones using mobile phones for making long-distance calls during the night or weekends, when
e) phones when using their mobile phones to make long-distance calls at night or on weekends, a time which.

OA: C

My question is that in option D , "they can avoid toll charges on their home phones using mobile phones for making long distance calls during..", does "using" modify "home phones" or it can jump over and modify "toll charges"?
I believe "home phones" is in prepositional phrase i.e. "on their home phones", and this prepositional phrase modifies the noun "toll charges". So I think "using" should modify "toll charges".

Thanks for your help!