Hello Marian!

Yes, you don't have to show an image. Just set 'Head Type' to 'none' in the 'Layout' tab.
To be more precise in my answer: make sure you select a theme style that does not require an image (like 'Original' or 'FullWidth'). 

Sorry, I misunderstood.

Latest News Enhanced Pro (LNEP) does not show photo captions. It only uses the 'alt text' if available in your article .

When clicking on an item, the article opens in a view created by the Contents component or the K2 component (if using K2). LNEP does not handle that part.

If your 2nd screenshot is actually a view of the article when it's open, you can just use CSS to hide the caption. An other option is to create a template override of the layout 'joomla/content/full_image.php'. But it seems like the layout is already overridden by your template to get the caption the way it is showing (it's not standard Joomla or you may be using K2?).

Ok, I understand that you have added the caption inside the actual text.
Same with the title, the event date... they are part of the article text (at least it looks like it).

Therefore, if you ask to show the article text in LNEP, it will have all that information.

I would suggest you add a meta description to your article (if you don't have that already) and use it as the text you show in LNEP.
There is no way LNEP can 'triage' what you want or no want to show from your article text the way it is setup.

You could also create a custom field of textarea or editor type that you could use as text to show in LNEP. Giving you full control of what you actually present.