Tails Greeter is a native Debian package.

Update POT and PO files

./setup.py build_i18n && \
   (cd po && \
       for po in *.po ; do msgmerge --update "$po" \
       tails-greeter.pot ; done \
   ) && \
   git commit po -m 'Update POT and PO files.'

Prepare a release

git checkout master && ./scripts/release.sh

… then follow the instructions, making sure you set the appropriate release on the first line of the new changelog entry.

Update the Debian package

Build a new Debian package (use a Stretch/amd64 chroot):

gbp buildpackage

If everything is fine, tag the release and push the changes:

gbp buildpackage --git-tag-only --git-sign-tags --git-keyid=$PGP_PUB_KEY && \
git push --follow-tags origin master:master

Add the Debian package to Tails

Sign the package:

debsign $CHANGES_FILE

Upload:

dupload --to tails $CHANGES_FILE