Yes, you can keep them on as long as you like. They are fully functional with the dock, and you can also keep them on while playing on the go.
Please make sure you have them installed correctly. Check that you followed the above installation instructions, as it is possible to attach them to the Switch in an incorrect position. Keep in mind the Switch will have a tighter fit in the dock, but this in no way hinders its performance or hurts the Switch or the dock.
Do not worry, all Nyko products have a warranty, just contact our customer support team here and they will help you get a replacement.