export your family tree in XML format in windows version and import it in new family tree in linux version.
I quoted this from gramps bugtracker where I reported this 'feature' 2 years ago, the answer was:
To use databases like that you need to have same version of db library
and their python binding on both system or they can be of newer
version on new system and gramps will try to upgrade them.
Your windows version of gramps had pybsddb-6.1.0 and db-6.0.30, your
linux version have pybsddb-6.1.0 and db-5.3.28 For things to work you
need linux db of same version as windows one or greater in which case
gramps will upgrade database.
Gramps uses both libraries from system so they can change anytime you
upgrade your system, except with windows and mac bundle which contain
their own version of those libraries.
Unless you know how to build and install them locally you must export
your family tree in XML format in windows version and import it in new
family tree in linux version.
In the ensuing conversation, you also have some insight on how to update the db on linux but I think I did the windows XML export in the end (but that was before version 5 was released).