Trek Roscoe 7 wheel wobble

No need to remove the tyre and tube to check if the wheel rim is out of true. Put a zip tie around the fork leg, cut the free end and position it so that it just touches the rim at one point (might as well pick where the valve is). Rotate the wheel slowly and observe what happens to the gap between the zip tie and the rim. That should tell you how far out if anything the rim is. If the rim is fine then it must be the tyre. It will either be a faulty moulding or a poor mounting. But you have to check the mounting first.

To check the mounting, look at the tyre where it meets the rim. There will be a thin line moulded into the tyre that should be a few mm away from the rim. The gap between the line and the rim should be constant. I have mounted tyres myself where the line varied considerably, often diving underneath the rim!

There are two ways that I know of to move the line, short of removing the tyre and starting again. One is to inflate the tyre to its max safe pressure (written on the tyre wall). That might force the tyre into position (usually with a loud BANG!) but it is not guaranteed.

The other way to move the line is to remove the wheel from the bike, deflate the tyre until it is quite squashy and only has a few psi left in it. Then move the tyre walls by hand. You may have to grab the tyre in both hands a few inches apart and wave the tyre up and down to get some extra torque on the tyre. But it will move. In the unlikely event of it not moving, let some more air out. If that doesn't do it (never failed for me), then you are going to have to start from scratch and hope you get it right.

Once the tyre is installed correctly, use the zip tie, this time on the tyre and see if the wobble is still there. It will not be perfect, tyres are moulded, not machined. If the wobble can be felt when riding then it is definitely too bad to be accepted, so you should return to the shop. I know that these days, not all bikes are bought from the LBS, so returning may be a right pain. But you cannot be expected to accept a bike where you can feel the wobble. An alternative would be to contact the seller tell them what you have done to diagnose and correct it and propose that you take the bike to an independent LBS and get them to take a look at it.