The privileges of the CRI(SE) are encompassed within the FI qualification. Occasionally the term CRI is used seperately in the context of being a ME CRI however; that is also encompassed in a FI (ME) qualification.
Under JAR-FCL the IRI qualification is exactly the same as the "removal of the no applied IF limitation" which is a hangover from UK National ratings. With the no applied IF restriction removed, you can subject to holding an IR and being standardised at an approved FTO, teach for an IR or subject to holding an IMC rating teach for that. If an approved FTO is looking for "IRIs" their only purpose would be to teach for an IR so it is probable that that is what they are looking for.
The CRI and IRI are actually stand alone qualifications.