Your quote should contain a clause that tells your prospect that your price etc, does not take TUPE into account, and that your price etc could vary depending on the exact contract that any employee who transfers over under the regulations is on.
I would also consider the reason that your prospect wants to change, why is she happy with the present cleaner, but not the company?
Although Pristine has given you his take, I would be very wary of taking this down the ETO route, without solid legal backing, although Dave is correct, in stating that its standard practice sometimes for the big players, they can indeed afford to bend the rules and pay the fines!
Regards,
Rob