How do I get purchased songs off iPod Touch without deleting the purchased songs from iTunes?

Okay, so I am now in possession of my mom's old iPod Touch, and it is linked to her iTunes account. My whole family has purchased songs through this account over the years. When I plugged the iPod into my iTunes, I selected "Manually manage..." and picked only the songs I wanted to go on the iPod. And yet, on the iPod there are 800 purchased songs that I don't want on there. This is confusing because when the device is plugged into my computer, under "Music" those songs aren't there - there are only the ones I manually put on there.

When I try to remove these purchased songs from the iPod itself, the only option is to actually delete the purchase. I don't want to do this because most of these songs weren't downloaded by me; I want the songs to be preserved on iTunes, I just want them off my iPod! Can anyone help me out? Thanks.