If the images in HTML are loaded from URLs, the converted PDF file doesn't include the images. If you want to include the images in the converted PDF file, please put the images to HTML as base64 data.
In order to confirm this situation, please see the following sample script. This sample script puts an image as URL and base64 data. The result is displayed them to a dialog and created a PDF file.
When you use this script, please copy and paste to the script editor of Spreadsheet.
Sample script :
function myFunction() {
// image
var url = "https://cdn.sstatic.net/Sites/stackoverflow/company/img/logos/so/so-icon.png?v=c78bd457575a";
var blob = UrlFetchApp.fetch(url).getBlob();
var b64 = blob.getContentType() + ';base64,'+ Utilities.base64Encode(blob.getBytes());
var html = "URL<img src=\"" + url + "\">Base64<img src=\"data:" + b64 + "\">";
var h = HtmlService.createHtmlOutput(html);
// Open dialog with the images.
SpreadsheetApp.getUi().showModalDialog(h.setWidth(500).setHeight(200), 'Sample');
// Create from HTML to PDF file.
DriveApp.createFile(h.getAs("application/pdf").setName("text.pdf"));
}
Result of dialog :
Both images can be seen.

Result of PDF file :
Only the image of base64 can be seen.

Note :
- This is a simple script. So please modify this to your environment.
References :
If I misunderstand your question, I'm sorry.