UMB FUND SERVICES, INC.

235 W Galena Street

Milwaukee, Wisconsin  53212

(414) 299-2000

July 24, 2017

Securities and Exchange Commission

100 F Street N.E.

Washington, D.C.  20549

Re:Hatteras Core Alternatives TEI Fund, L.P.

Registration No:  811-21665

Filing pursuant to Rule 30b2-1 and Section 24(b) of the Investment Company Act of 1940

Dear Sir or Madam:

On behalf of the above-named registrant (the “Fund”) and pursuant to Rule 30b2-1 and Section 24(b) under the Investment Company Act of 1940, as amended, is amendment to the Fund’s Form N-CSR for the annual period ended March 31, 2017 that was filed on June 9, 2017.  The following change is reflected in this filing:

1.Hatteras Master Fund, L.P. Financial Statements — Other Information (Unaudited)

On page 22 of the financial statements of Hatteras Master Fund, L.P. (the “Master Fund”) in the contents of Other Information, disclosure was added for the board of directors’ approval of the interim sub-advisory agreement and sub-advisory agreement of the Master Fund under the section heading “SUB-ADVISORY AGREEMENT”.

Sincerely,

/s/ Terry Gallagher

Terry Gallagher

EVP / Director of Fund Accounting and Administration

Encl.