My estate agent just got me a stamped TM30 form and advised me to keep it in my passport. There is no statement on the form to the effect that it must be kept in the passport. Does anyone know if this is a requirement?

No you don’t need to keep it in the passport. But you should keep it safe in case immigration require proof that the report was made.

In my experience at the TM-30 office in Jomtien-immigration - if you get it in person, they staple it to the last-page of your passport.