Hello,

I have checked the Compare and Wishlist in both conditions: as a logged-in user and logged out:

I do not see any problems with the Compare and Wishlist:

Compare list: https://gyazo.com/7c9485e7e57c08f5752a90dc22224ea0

Wishlist: https://gyazo.com/2cd82dee7eb28c28ca224a6dfefd65ab and https://gyazo.com/16ac5adfe54b37dd084377b0183ff924

It is not possible to insert the text in the place you show in the screen with Woocommerce/WoodMart default options.

Best Regards