When Jenkins is configured to remember passwords on a Rebuild, it remembers Non-Stored Password Parameters as well as normal Password Parameters.

According to the description of the configuration option, it should not remember Non-Stored Passwords:

If the remember password option is checked, the rebuild plugin will use the stored password parameter when a rebuild is triggered. If the remember password option is unchecked, the user will be prompted to enter the password every time a rebuild is triggered. This only applies for a parameterized build with parameters of type password.

A simple test shows that this option also remembers Non-Stored Password Parameters.

1. Set up a simple job with a Non-Stored Password Parameter
Example code:

node("master") {
    println(params.PASSWORD)
}

2. Build the job once as User A with parameter "test"
3. See "test" printed to console
4. Rebuild the first build
5. See "test" printed to console
6. Switch to User B
7. Rebuild the build
8. See "test" printed to console

The Non-Stored Password should not persist across Rebuilds. This issue is marked as "Minor" because the workaround is to disable the top-level configuration to Remember Passwords.