The other issue that could be happening is that the ID of the image has changed from one site to the other. If you used a standard export/import to move things then the post IDs on the new site will not match the post IDs on the old site. When moving a site you must ensure that all posts maintain the same IDs and this cannot be don by exporting and importing, you’ve basically got to copy the DB as is.
Again, this comes down to how the site was migrated.
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