A brief thank-you note after a recruiter screen is optional, not a requirement.

If the conversation was substantive or the recruiter gave you useful guidance, a short note can be professional and reinforce your interest.

Do not send a long recap or use the note to add information that should have been in the application.

Skipping the message is unlikely to determine the outcome; your candidacy matters far more than a courtesy email.

I send one if the conversation was actually useful, not after every administrative call.