Splitting the login between text and email feels safer, but both pieces usually end up on the same phone and in the same cloud backup. Deleting the conversation may still leave notification previews, screenshots, synced tablets, or backups behind.
Since your concern is the password sitting in writing, the simple low-tech option is a phone call. Read it aloud while your sister types it directly into the streaming app on the TV. Avoid voicemail, call transcription, and entering it through a shared computer browser, since the browser may save or sync the login without anyone noticing.
Before doing that, make sure this password is used only for the streaming service. If it matches your email, shopping, or banking password, change it first. Sharing a reused password turns a minor streaming-account issue into a much bigger problem.
I agree with the device-code suggestion when the service provides it, but check what the code actually does. You should be authorizing the TV from your own phone, not signing your whole account into a browser on your sister’s phone. Once it works, have her use a separate profile so your watch history, recommendations, and “continue watching” list do not become a family argument. Lock your own profile if the service supports that.
When she leaves, remove the parents’ TV through the account’s device page. Then open the streaming app on that TV if possible and make sure it no longer goes straight into your account. Some apps keep the account email or profile names on the login screen even after the session is revoked, so clearing the app data or reinstalling the app may be worth doing.
I would not automatically change the password afterward if you entered it through an official TV activation code and removed the device. If you spoke the password aloud, typed it into an old smart TV, or used a shared browser that offered to save it, changing it is the cleaner option. Just expect to sign your own TVs back in afterward.