Hidden text for Mobile
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How do search engines respond to text that is hidden on mobile settings online.
I have a
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I really think that it is debatable. You want to have a good user experience so you want to display the text to them in an aesthetically pleasing way, but you don't necessarily want to hide it because that is no good for the engine. When choosing between good for the searcher or good for the engine, I would pick whatever is good for the searcher. Can you add some coding to display it differently on a mobile device, perhaps add the content below the image instead?
As far as penalized, it is hard to say. How is the rest of your content on page? Is it quality? On the grand scheme of things, this could be really small in your overall SEO success. You have to make the decision on what is more important to you, customer or engine.
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It's very common for responsive sites to reduce the content for mobile devices, without any penalty. This is not a deceptive or black/gray hat tactic, as long as you're not cloaking the text. In fact, you're just making a better UX.
In my experience, the hover-state text will be indexed (as a link). You can see an example on my company's work page here - notice how the hover-state content reduces as the site responds to different devices. Also see how the hover-state text is showing (as links) in the cached version of the page.
I hope this helps!