HDPE can be recycled (as many thermoplastics can) but once it's in a matrix of other stuff (say calcium) it get's really difficult to do so. Also HDPE is not biodegradable. It can break up into microplastic, but I wouldn't call that exactly enviromentally friendly. Maybe if there are some added enzymes or something…
But you can just use unbleached, recycled paper. Paper is easy to recycle, doen't require a lot of chemicals (unless you bleach it) and is already one of the most recycled resources.