No, they have never made such a claim.
From the USPTO Trademark Manual of Examining Procedure....
https://tmep.uspto.gov/RDMS/TMEP/current#/current/TMEP-1200d1e7600.html
The Trademark Trial and Appeal Board has held that the addition of the prefix "e" does not change the merely descriptive significance of a term in relation to goods or services sold or rendered electronically, where the record showed that the "e" prefix has become commonly recognized as a designation for goods or services sold or delivered electronically. In re Int’l Bus. Machs. Corp., 81 USPQ2d 1677, 1679 (TTAB 2006) ("We see no difference in the meaning or connotation of ‘e-server’ and ‘eserver,’ and consider them both to be an abbreviated form of ‘electronic server.’");
In re SPX Corp., 63 USPQ2d 1592 (TTAB 2002) (E-AUTODIAGNOSTICS merely descriptive of an "electronic engine analysis system comprised of a hand-held computer and related computer software");
In re Styleclick.com Inc., 57 USPQ2d 1445 (TTAB 2000) (E FASHION merely descriptive of software used to obtain beauty and fashion information, and for electronic retailing services);
Cont'l Airlines Inc. v. United Airlines Inc., 53 USPQ2d 1385 (TTAB 1999) (E-TICKET generic for computerized reservation and ticketing of transportation services).
Similarly, with appropriate evidence, the prefix "i" or "I" was held to be understood by purchasers to signify Internet, when used in relation to Internet-related products or services. See In re Zanova, Inc., 59 USPQ2d 1300 (TTAB 2000) (ITOOL merely descriptive of computer software for use in creating web pages, and custom design of websites for others). In these situations, the examining attorney should provide evidence of use of the prefix "e" or "i" in relation to the goods or services.
https://www.wipo.int/amc/en/domains/search/text.jsp?case=D2013-0510
Frank Michael Weyer v. DomainSource.com, Inc.
WIPO Case No. D2013-0510
...
Respondent is DomainSource.com, Inc. of Lakehead, California, U.S., represented by John Berryhill, U.S.
...
The disputed domain name consists of a common word, “shades”, preceded by the letter “i”, which is commonly used to refer to availability via the Internet and is part of a portfolio of domain names made up of common words and phrases.
