Hi Carlosnulla, and welcome to the forum.
First of all, can I clarify that you and your wife are resident in the UK. The rest of my response is written on the basis of UK law, so if you live elsewhere, you will need to get advice from a local source in your jurisdiction.
Unfortunately the fact that this image may have been used on a personal blog, with no commercial motive and with relatively few views, makes no difference the fundamental liability for making a copyright-protected image available to the public without permission. The fact that individual image was used within a collage is also irrelevant to the basic claim of infringement.
However when you say that your wife used the image because she was commenting of the original article from which she obtained the image, that
may mean that she used the image within the exception provided in
Section 30(1) of the Copyright Designs and Patents Act 1988, that is to say it was used for the purpose of criticism or review of the article for which this screenshot constituted the headline. This defence is very context specific and would only apply if she was clearly reviewing or critiquing the article. It would not apply if, for instance, she was criticising the behaviour of, say, Jack Dorsey, or Twitter. The thing that she was reviewing must have been a work (of literature, reportage etc) which itself was subject to copyright, although it doesn't have to be the photograph itself. And the other essential factor is that your wife's posting itself should not have been reporting the news. This latter point is important because the use of photographs in connection with news reporting falls outside the section 30 exception (see susection (2). Your wife would not have been reporting the news if she was merely referring to facts or opinions etc which were already known. However if she introduced some new fact (say a previously unreported quote from one of the people referred to in the article) then that might well mean that her blog post was news reporting even though she was not a journalist etc.
As you can see, this is fairly technical stuff, and undoubtedly you would need a lawyer to argue this on your behalf if the matter went to court. However I don't think this will ever go to court, so much will depend on your resolutiion in the face of the threats from PicRights. They have no in-house legal team and so won't be able to judge the strength of your defence if you argue that your wife's use fell within the Section 30(1) exception. They will continue to ignore your response and stick to their script. So be prepared for a long tussle before they eventually give up or their outside lawyers tell them it's a hopeless case.
If you decide, for understandable reasons, that you don't want the stress of protracted demands from PicRights, you can make a counter offer, which of course should be based on the standard Reuters fee of £101.50, and not the inflated £370 demand which is only designed to make a profit for PicRights. Obviously if you can find the same image availble for a lower licence fee on another site like Alamy, (which often happens with Reuters' images) use that lower fee as the basis of a counter-offer. You are only liable (assuming the section 30 exception doesn't cover the circumstances) for damages equal to the actual loss the copyright owner has suffered through not having sold a valid licence at the fair market rate. I didn't find the same image on the first 3 of 15 pages of Jack Dorsey images on Alamy, but that doesn't mean it isn't there.
