Even if they did look at your phone there is no worry. Rooting is not illegal. It is only bad for issues like warranty purposes. At most I would remove any tether apps, as they may not like those. Not sure what they would do or say.
Dont even know why they'd need to look at your old phone TBH.
If they say they'll move your contacts for you just say that they're all on google and will sync when you activate.
If they want to move your media just say you can swap the SD cards.