To pull your file from your archive, you can use tar xzf archive.tar.gz my/path/to/file.txt. Note that the directories in the file’s path will be created as well. Use tar t (i.e. tar tzf archive.tar.gz) to list the files in the archive.
tar does not support “in-place” updating of files. However, you can add files to the end of an archive, even if they have the same path as a file already in the archive. In that case, both copies of the file will be in the archive, and the file added later will override the earlier one. The command to use for this is tar r (or tar u to only add files that are newer than the archive) is the command to use. The . in the path should not be a problem.
There is a catch, though: you can’t add to a compressed archive. So you would have to do:
gunzip archive.tar.gz tar rf archive.tar data/data/com.myapp.backup/./files/settings.txt gzip archive.tar
Which is probably not what you want to hear, since it means rewriting the entire archive twice over. If it’s not a very large archive, it might be better to untar the whole thing and then re-tar it after editing. Alternately, you could use an uncompressed archive.
gzip -dc archive.tar.gz | tar -r data/data/com.myapp.backup/./files/settings.txt | gzip >archive_new.tar.gz