Not display an image of category of custom post

First of all $category->$term_id is wrong use $category->term_id

I don’t think $category->$term_id will give you the desired result

For this you must have create some meta for the image in the backend.

term_image_id = get_term_meta( $category->term_id, 'your-term-id', true );

Here the term id is $category->term_id and the term value is your-term-id

Can you please check if that works or not?