If an image is uploaded to Linnworks inventory as Primary Image, Image1, Image2 and so on, then this image is hosted on our image servers.
If the image URL is specified in the Extended Properties, then this image remains hosted by the external source, and Linnworks just uses its URL to pass it to the channel when creating or updating a listing.
When an item is listed on eBay, then its main images on the listing are hosted by eBay. Regardless of where the image was hosted previously, once the listing is created the gallery image is uploaded to eBay servers. As for images in the HTML description, they remain hosted where they were - external server or Linnworks servers.