Exhibit 23.3

Consent of Independent Registered Public Accounting Firm

We consent to the inclusion in the Registration Statement on Form S-1 of Pilgrim Bancshares, Inc., the Form FR Y-3 filed with the Board of Governors of the Federal Reserve System by Pilgrim Bancshares, Inc., and the letter applications filed by Conahasset Bancshares, MHC (the “Company”) with the Massachusetts Commissioner of Banks and the Board of Governors of the Federal Reserve System in connection with the Company’s proposed mutual to stock conversion (collectively, the “Regulatory Applications”), of our report dated March 6, 2014, on our audits of the consolidated financial statements of Conahasset Bancshares, MHC and Subsidiary as of December 31, 2013 and 2012, and for the years then ended, appearing in the Prospectus, which is a part of this Registration Statement on Form S-l and the Regulatory Applications. We further consent to the reference to us under the heading “Experts” in such Prospectus.

SHATSWELL, MacLEOD & COMPANY, P.C.

West Peabody, Massachusetts

March 11, 2014