In general, Google doesn’t like it when you serve a different version of your pages to googlebot than to all other visitors. But this might be case where you could have your theme “skip the skip” if user-agent happens to be googlebot. That would be the quick fix.
Do you make sure to include SEO fields for summary and have an excerpt made for each page? If google wants to highlight a couple of words that weren’t in the excerpt, it still might show a different part of the page, but this way you’d be able to make your standard page excerpt for google by hand (and obviously without the “skip” message…).
EditAdd: SEO capabilities may come directly in your theme, or may be added with a SEO plugin.
Thank you for reply Tor – I have never heard of an excerpt for each page being deliberately specified. Do you mean by utilising an application such as Yoast?
I hadn’t thought of using it for this site as it is a very small site, virtually only one page but perhaps I will now. Thanks.
Some themes may simply put the_excerpt() as a page description, defaulting to first some 150 characters of the content. But, obviously, your themes doesn’t seem to be doing that.
Good luck
/Tobi