Recruiter is asking me for a reference after successful hire

My recruiter is asking me for a reference.

They told me that they do this to everyone after a successful hire.

They say it's for their "internal process" and they seem really pushy about it.

What does it really mean? Is there any harm in sharing my references to the recruiting agency even after landing the job.

I would understand if it's my current employer who's asking, but it was the recruiting agency.

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