Hey @jclin10, let's jump right into this!
The first thing you need to check is your selective sync settings, in order to make sure your folders are syncing locally on the device.
Apart from that, feel free to also have a look at the file's status, and icons in order to make sure they're syncing as "available offline" and not online-only.
For your laptop, you want to check the same exact settings, just make sure that you're unchecking the folders you’d like removed (with selective sync) and that you use online-only for your files.
Keep in mind that for available-offline, and online-only files and folders might not be available to all Basic, and Windows users.
In that case, you can always use selective sync.
If you have any questions, let me know!