It would be useful to have a custom text in Post/ZipCode popup, explaining to the user the purpose of the popup.

Sample text: Check if we deliver in your area. Select your zip code from the list below

Now I’m achieving it without core edits using the following CSS snippet:

.wppizza-dbp-areas:before {
content: "Verifica se consegniamo nella tua zona. Seleziona il tuo CAP dall'elenco sottostante";
text-align: left;
display: block;
}

Adding a WYSIWYG field in admin area would be enough,