A company tutor wishing to go private

I work as an independent contractor/tutor in LA for a tutoring company. The company is headquartered in Wyoming and the local office is in Lancaster. [I tutor in students' homes.] I recently learned through a student-client that his school would be an excellent student body for recruiting new students for tutoring. I would like the freedom to do so privately, independently, but believe the non-compete agreement I signed when I signed up with this company may curtail this. All agreements I've ever read or signed do not prohibit a tutor from tutoring outside the company -- making a living as a tutor for a single company is not possible -- but would this be considered 'outside' if the original contact was made through a company-referred student? I don't wish to do anything that carries even the slightest hint of impropriety -- but, as a laid-off teacher, I so need the money I could make from this client base. My current split for a session is 35-40% of the cost. And: If it could be done, how could it be done?

Thank you to any/all who can give me advice/perspective on this subject.