I've also run afoul of Getty Images in the same way...
They never sent a cease and desist letter,
just a demand for $1000 US for the use of a thumbnail
found on Google Image Search.

I removed the image and ignored them.

The later sent an additional letter (with a screen shot of
their image on my page) again demanding payment of
$1000 US.

I ignored it.

I have not heard from them since, and doubt seriously
if a court would award them any damages.

The letter your client received (while it LOOKS like it's from
a 'solicitor' (in American that's a lawyer) is really from a
debt recovery company... Getty has turned over the
account to a collection agency.

Personally, I'd ignore this too. I think this is a scam
through which Getty Images makes a good deal of
its income, by intimidating and harrassing people.

They do not use the standard methods of contact
when an image they have license to is found on a site,
they move right into the demand for payment, and offer
no options. Most people who end up with these images on
their sites are not consciously infringing, and for that
reason deserve the benefit of the doubt.

One thing it DOES do, is bring home the idea that if
you are going to put other peoples images on your sites,
don't depend on Google Image Search for content.

I recommend istockphoto.com for excellent, professionally
photographed stock photography at reasonable prices.

- Puamana