Ah! OK, I see what you mean. It is the browser doing that. It takes the image tag’s “title” attribute and transforms it into what is usually called a “tool tip”.
FancyBox does not create not use this title attribute.
To get rid of the browser tool tip, you’ll need to get rid of the image tag title attribute and in both examples these attributes are created by another plugin:
1. On the gallery page I would think it’s the NextGen Gallery plugin that takes the image file name (without .JPG) by default. You might look in either the general plugin settings to disable this behavior or you’ll have to edit each gallery item to remove or alter this attribute. Note that it might even be called differently in the settings.
2. On the other page, it looks to me like those are image elements created by the WPBakery page builder plugin. It creates both a “title” and “alt” attribute for each image tag. You could take a look at each of these elements to see if there are fields that correspond with each tooltip text. If there’s only one, then clear it and both the title and alt should disappear. Removing the alt attribute is not optimal (for SEO and accessibility reasons) but removing the title attribute will get rid of the tooltip. if there are two fields, then clear one of them, save and check the front-end to see if that’s the one. If the tooltip does not disappear, fill the field again and clear the other 🙂
Sorry I cannot tell you exactly how to proceed. I’m not familiar with either of these plugins. You might get better info on their respective support forums.