unknownrebelbang - that was my point too. Cheques will cost her money if she has a business account therefore she gets less pay per student who pays by cheque. If this is weekly for relatively small amounts, then her loss is greater. As a business, she would probably have to pay to lodge cash as well, but cheques cost more as they have to be processed manually afaik (correct me if I'm wrong though).
Ds1's tutor works all hours tutoring outside of school hours including weekends so this is probably her sole income as she is always available on the phone during school time.
I do think it a bit extreme however, to hand cheques back. Rather better to have accepted them, but ask for cash in future.