Well, I am very pleasantly surprised by Apple's way of dealing with this. I did contact the Help system, went through all the hoops to get to the right place and put in a description of what the app. does and doesn't do, being promised a reply by email, but that turned out to be unnecessary. When the iTune invoice appeared, it had a link for 'Any problems?'. I clicked it and was presented with a number of tick-boxes. I ticked the one for 'App does not do what it should do' (or words to that effect), and very soon received confirmation that my purchase price would be refunded, no questions asked.
I am glad about this, not because of the actual money involved (which, in the greater scheme of things, is after all pretty small), but because of Apple's respect and consideration for customers and users of Apple equipment.
Thank you both for advice and support.