I think the previous poster is quoting issue 4 of the standard.
The relevant section of the BRC Global Standard for Packaging and Packaging Materials Issue 5 July 2015 is:
3.7 MANAGEMENT OF SUBCONTRACTED PROCESSES
Where any process steps in the manufacture of the packaging material are subcontracted to a third party or undertaken at another site, this shall be managed to ensure it does not compromise the quality, safety or legality of the product.
3.7.1 The use of subcontractors and the status of the subcontractor with respect to the Standard shall be notified to the brand owner and/or customer.
3.7.2 Where any processes are subcontracted, including artwork or pre-press activity, the risks to the quality and safety of the product shall form part of the hazard and risk analysis and the company’s evaluation of the system shall be held on record.
3.7.3 Clear specifications shall be agreed for all work outsourced to a subcontractor.
3.7.4 Where any process steps in the manufacture of the packaging or packaging material are subcontracted, final release of the product shall remain the responsibility of the site.
Controls shall be in place for checks on finished work to ensure product safety and quality meets specification prior to dispatch to the final customer.
So you should have supplier approval documentation, your hazard analysis should include this contracted work and appropriate controls applied. There should be agreed specifications, checks on the finished work and evidence of final release by yourselves. You also need to consider how you meet the requirements of 5.2 GRAPHIC DESIGN AND ARTWORK CONTROL.