Cover Letter to Offer to Purchase and Letter of Transmittal

IF YOU DO NOT WANT TO TENDER YOUR LIMITED PARTNERSHIP INTERESTS FOR REPURCHASE AT THIS TIME FOR ANY REASON, PLEASE DISREGARD THIS NOTICE. THIS IS SIMPLY NOTIFICATION OF THE FUND’S TENDER OFFER.

October 21, 2015

Dear Investor of The Endowment Institutional TEI Fund W, L.P.:

We are writing to inform you of important dates related to the tender offer by The Endowment Institutional TEI Fund W, L. P. (the “Fund”). If you are not interested in selling your limited partnership interests at this time, please disregard this notice and take no action.

Please note that the sale of your limited partnership interests may be subject to a 2% Early Redemption Fee if you decide to sell your interests in this offer.

The tender offer period will begin on October 21, 2015 and end on November 20, 2015. The purpose of the tender offer is to provide liquidity to investors who hold limited partnership interests. Limited partnership interests can be repurchased by means of a tender offer only during one of the Fund’s announced tender offers.

Should you wish to sell any of your limited partnership interests during this tender offer period, please complete the enclosed Letter of Transmittal (the two page Tender Offer Form will suffice) and contact your financial advisor who services your account for specific return instructions. Allow for additional processing time by your financial intermediary if necessary as the form must ultimately be received by the Fund’s Investment Adviser, Endowment Advisers, L.P. either by mail or by fax in good order by midnight, Central Standard Time, on November 20, 2015. If you do not wish to tender limited partnership interests for repurchase for any reason, simply disregard this notice. No Action is Required if You Do Not Wish to Tender Your Interests for Repurchase at This Time.

For additional important information regarding the tender offer, please refer to the attached Offer to Purchase document. We look forward to resuming the implementation of a regular tender offer process in the future and will provide further details on this process as they become available. If you have any questions, please contact your Financial Advisor or call the Support Desk of the Investment Adviser at (800) 725-9456.

Sincerely,

The Endowment Institutional TEI Fund W, L.P.