I can't speak for the Greece tour but last year I did South of Italy. Cow diary, nitrates/nitrites, nuts (small amount OK), more than one glass of wine set off my IBS, plus I am allergic to chocolate. I was careful with what I ate. If I ate cheese at one meal because I couldn't pass up the bufalo mozzarello, I wouldn't eat cheese the rest of the day. Restaurants and hotel breakfasts had soy milk for my coffee.
Before going to Italy I learned how to ask in Italian for coffee with soy milk, no chocolate, sorbetto instead of gelato and no cheese. It was not difficult to avoid my trigger foods. Either on your translator app or on an index card in phonetic Greek and written Greek make notes how to request what you can eat and what you can't eat. You can show the card to the waiter when eating on your own. Let your Rick Steves guide know of your food limitations so she/he can help you.
Most of all, don't make a big issue out of being served something you can't eat. If served, don't eat it or politely decline. You may need to order something on your own but I doubt it. There is so much food served at meals that you won't go hungry.
Also, I was concerned about potty stops on bus days. Not an issue since we stopped every 1 1/2 hours.