If the URL is not an absolute path(without https/http), SharePoint will automatically fill in the URL.
You could save your pictures in SharePoint library directly.And add the relative or absolute path of the image in SharePoint to the code.
My site url is：https://contoso.sharepoint.com/sites/dev
URLs and tokens in SharePoint
This may be a defect of IE itself
Being an old browser, IE 11 lacks a few features like fetch, map, and proxy. During SPFx development we normally make use of these features and they fail to work in IE 11.
Please see if the article below is helpful to you:
IE 11 Polyfill Package For SPFx