For now, if you export the words you’ve studied your tutor should be able to get a sense of what you’re studying. You could also consider creating custom study decks that contain words and phrases you’re learning with your tutor. The more outside context you can add to a list of word the better they’ll stick in your long-term memory!
Back when I was very actively studying Chinese, I maintained study decks where I would add a new section every week with all the new stuff I was learning. Personally, my process was always starting from context (book, song, classroom, etc.) and adding to Skritter–not the other way around.
Also, have you tried starring things you’re struggling with, or just keeping a note of stuff that has you confused on Skritter? It’s a great way to discuss the finer details of synonyms, grammar points, etc. and get max value out of the 30-minute or one-hour tutoring session.