Exhibit 99.6

March 11, 2014

Board of Trustees

Conahasset Bancshares, MHC

Boards of Directors

Conahasset Bancshares, Inc.

Pilgrim Bancshares, Inc.

Pilgrim Bank

40 South Main Street

Cohasset, Massachusetts 02025

Re: Plan of Conversion

Conahasset Bancshares, MHC.

Members of the Boards:

All capitalized terms not otherwise defined in this letter have the meanings given such terms in the Plan of Conversion the (“Plan”) adopted by the Board of Trustees of Conahasset Bancshares, MHC (the “MHC”). The Plan provides for the conversion of the MHC into the stock form of organization. Pursuant to the Plan, the MHC will be merged into Conahasset Bancshares, Inc. (the “Mid-Tier”) and the Mid-Tier will merge with Pilgrim Bancshares, inc., a newly-formed Maryland corporation (the “Company”) with the Company as the resulting entity, and the MHC will no longer exist. As part of the Plan, the Company will sell shares of common stock in an offering that will represent the ownership interest in the Mid-Tier now owned by the MHC.

We understand that in accordance with the Plan, depositors will receive rights in a liquidation account maintained by the Company representing the amount of (i) the MHC’s ownership interest in the Mid-Tier’s total stockholders’ equity as of the date of the latest statement of financial condition used in the prospectus plus (ii) the value of the net assets of the MHC as of the date of the latest statement of financial condition of the MHC prior to the consummation of the conversion (excluding its ownership of the Mid-Tier). The Company shall continue to hold the liquidation account for the benefit of Eligible Account Holders and Supplemental Eligible Account Holders who continue to maintain deposits in Pilgrim Bank. The liquidation accounts are designed to provide payments to depositors of their liquidation interests in the event of liquidation of Pilgrim Bank (or the Company and Pilgrim Bank).

In the unlikely event that either Pilgrim Bank (or the Company and Pilgrim Bank) were to liquidate after the conversion, all claims of creditors, including those of depositors, would be paid first, followed by distribution to depositors as of December 31, 2012 and depositors as of the last day of the calendar quarter immediately preceding the date on which the Federal Reserve Board (“FRB”) approves the MHC’s application for conversion, of the liquidation account maintained by the Company. Also, in a complete liquidation of both entities, or of Pilgrim Bank, when the Company has insufficient assets (other than the stock of Pilgrim Bank), to fund the liquidation account distribution due to Eligible Account Holders and Supplemental Eligible Account Holders and Pilgrim Bank has positive net worth, Pilgrim Bank shall immediately make a distribution to fund the Company’s remaining obligations under the liquidation account. The Plan further provides that if the Company is completely liquidated or sold apart from a sale or liquidation of Pilgrim Bank, then the rights of Eligible Account Holders and Supplemental Eligible Account Holders in the liquidation account maintained by the Company shall be surrendered and treated as a liquidation account in Pilgrim Bank, the bank liquidation account and depositors shall have an equivalent interest in such bank liquidation account, subject to the same rights and terms as the liquidation account.

Washington Headquarters Three Ballston Plaza 1100 North Glebe Road, Suite 600 Arlington, VA 22201 www.rpfinancial.com   Telephone: (703) 528-1700 Fax No.: (703) 528-1788 Toll-Free No.: (866) 723-0594 E-Mail: mail@rpfinancial.com

RP^® Financial, LC.

Board of Trustees

Boards of Directors

March 11, 2014

Page 2

Based upon our review of the Plan and our observations that the liquidation rights become payable only upon the unlikely event of the liquidation of Pilgrim Bank (or the Company and Pilgrim Bank), that liquidation rights in the Company automatically transfer to Pilgrim Bank in the event the Company is completely liquidated or sold apart from a sale or liquidation of Pilgrim Bank, and that after two years from the date of conversion and upon written request of the FRB, the Company will transfer the liquidation account and depositors’ interest in such account to Pilgrim Bank and the liquidation account shall thereupon become the liquidation account of Pilgrim Bank no longer subject to the Company’s creditors, we are of the belief that: the benefit provided by the Pilgrim Bank liquidation account supporting the payment of the liquidation account in the event the Company lacks sufficient net assets does not have any economic value at the time of the transactions contemplated in the first and second paragraphs above. We note that we have not undertaken any independent investigation of state or federal law or the position of the Internal Revenue Service with respect to this issue.

Sincerely,

RP^® Financial, LC.