Taxonomy terms does not have images by default. As I can see it must be a feature of your theme.
It's definitely not a custom field, only posts/custom post types can have them.
However if you can ask the theme developer how to get the term image based on the term id, then I might be able to put something together for you.
There must be a funtion like get_term_image_by_id($term_id) or something similar defined somewhere. Once we have that, it's going to work.Best,
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