Yes: sorry for naming the "host application" a 3rd party - let's say it's a CMS like Prestashop of whatever.
Usually, as the uStore Connect password is the same for all users (as I wrote above), our customers do not store it in the Host application's database (per user), as it would make useless duplicates.
Instead, they store it in a server-side configuration file of the Host application - or, why not, in a specific "configuration" record in the database, if they like it.
"Clear or not clear?" Anyhow, the call to the uStore Connect API is made via HTTPS, so it's not so different than a user typing a password "in clear" in a Login page field. Now, if the Host application developer prefers hashing the password, store the hashed value in his configuration file / configuration record, then unhash it, when he/she needs to call the uStore Connect API, for sure it's an extra security.