If the tiles have been laid correctly then they would have been laid on a tackifier adhesive, which would have been applied with a flat trowel or a roller - it is such a thin skim there will be nothing to scape up, plus it will have impregnated the concrete sub-straight.
If they have been laid incorrectly on a general purpose adhesive then you will be forever scraping up the residual adhesive and there will still be impregnation of the sub-straight.
I admire your tenacity of not walking away from a job - but you asked for advice and I have offered it, I would latex it or politely decline.
Steve