I tried a couple of things but none seem to have worked.
I used the following command to copy the dump file into the container.
docker cp ./db.dump a2198b1e36e5:/var/lib/neo4j/import/db.dump
And then I used the following to load it into the db.
docker run --interactive --tty --rm \
--volume=$HOME/neo4j/data:/data \
--volume=$HOME/neo4j/backups:/backups \
neo4j/neo4j-admin:4.4.9 \
neo4j-admin load --database=neo4j --from=/var/lib/neo4j/import/db.dump
But it threw and exception that the database must be stopped before loading the dump file.
Interestingly enough I can't stop the database because it's not enterprise version.
STOP DATABASE neo4j; // fails with error "Unsupported administrative command.."