First, check to be sure that your tube has this flag on it:

Our transition to the recyclable tube is happening throughout 2019 and 2020, so not all tubes will immediately be recyclable. It's important that if your tube does not have this flag on it that you don't put it into your recycling bin.
Your tube has the flag above on it? Great! Getting your tube ready for recycling is easy: simply squeeze out as much of the toothpaste from the tube as you can, replace the cap, and place the tube in your recycling bin. The Tom's of Maine toothpaste tube can be put into your household recycling bin for curbside recycling if your community accepts #2 HDPE plastic. #2 plastic is a commonly recycled plastic and is what many laundry detergent bottles and milk jugs are made from.
Please don't cut open the toothpaste tube to try and remove excess toothpaste! During the processing of the tube at the recycling facility, the tube is ground up and goes through a "rinsing" process, where all the residual toothpaste is washed off of the plastic. So there's no need for you to do any rinsing at home.