The police said they aren't able to take them.

Left behind where?

At a motel. The person is aware where they are just to slack to come and get them. Don't won't to be hanging onto these forever.
Unable to read any of the markings on the container.

If it were a pair of shoes I'd just throw them away... but with something that sentimental, I'd encourage you to contact the person again - inviting them to come and get them...

Then stash them in a corner somewhere.

... I would just feel weird about discarding human remains.