I would like a combination mark: a word mark + an abstract symbol.
I was playing around with logo lettering and symbolism ideas. One cool idea I had was to make the two ts of "tutors" into the pi (math) symbol.
Another idea I had was to insert the shape of a pencil at the end of the company name, as though it had been written by a student with neat penmanship.
I like the idea of having the name of the company in script... It's like in the old days when students and teaches actually used to write in script. On the other hand, print looks more modern and neater.
Also - if not doing the pi symbol, I would offer tutors to begin with a lower case letter (since it's a verb; it's not that I have a collective of tutors).
I also might like a geometry symbol (circle, triangle, trapezoid, circle with bisectors) as a background image.