Listing Designer includes two template editors, each with a different way to set the header images size:
New templates (not labeled 'classic')
Make images responsive with New templates:
After uploading an image to a content block:
Click the image and select the ruler button:
Set the Width to 100%, and
set the Height to auto
After clicking Update, your image will adapt to any screen size.
Make header image responsive with Classic templates:
this feature is currently only available for templates with large background image headers. Templates such as "Boxed" do not have the option below.
Hover over the large background header image to reveal the Zoom settings.
Then, select the multi-axis Fit button:
The first two Fit buttons are used for a background images that crop when the screen gets smaller.
Now, the header image will be full-width and adapt to any screen size: