You need not to change the class file, simply add the \renewcommands in your letter code.
Please note that the current version of class moderncv is 2.0.0. The github repository you linked to uses an outdated version! Better use the current one!
With the following MWE
\documentclass[11pt,a4paper,sans]{moderncv}
\moderncvstyle{classic} % casual, classic, banking, oldstyle and fancy
\moderncvcolor{blue}
\renewcommand*{\addresssymbol} {} % <=============================
\renewcommand*{\mobilephonesymbol} {}
\renewcommand*{\fixedphonesymbol} {}
\renewcommand*{\faxphonesymbol} {}
\renewcommand*{\emailsymbol} {}
\renewcommand*{\homepagesymbol} {}
\renewcommand*{\linkedinsocialsymbol}{}
\renewcommand*{\twittersocialsymbol} {}
\renewcommand*{\githubsocialsymbol} {} % <=============================
\usepackage[utf8]{inputenc}
\usepackage[scale=0.75]{geometry}
% personal data
\name{John}{Doe}
\title{Resumé title}
\address{street and number}{postcode city}{country}
\phone[mobile]{+1~(234)~567~890}
\phone[fixed]{+2~(345)~678~901}
\phone[fax]{+3~(456)~789~012}
\email{john@doe.org}
\homepage{www.johndoe.com}
\social[linkedin]{john.doe}
\social[twitter]{jdoe}
\social[github]{jdoe}
\extrainfo{additional information}
\photo[64pt][0.4pt]{example-image-a}
\quote{Some quote}
\setlength{\footskip}{66pt}
\begin{document}
%----- letter ---------------------------------------------------------
% recipient data
\recipient{Company Recruitment team}{Company, Inc.\\123 somestreet\\some city}
\date{January 01, 1984}
\opening{Dear Sir or Madam,}
\closing{Yours faithfully,}
\enclosure[Attached]{curriculum vit\ae{}}
\makelettertitle
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Duis ullamcorper
neque sit amet lectus facilisis sed luctus nisl iaculis. Vivamus at neque
arcu, sed tempor quam. Curabitur pharetra tincidunt tincidunt. Morbi
volutpat feugiat mauris, quis tempor neque vehicula volutpat. Duis
tristique justo vel massa fermentum accumsan. Mauris ante elit, feugiat
vestibulum tempor eget, eleifend ac ipsum. Donec scelerisque lobortis
ipsum eu vestibulum. Pellentesque vel massa at felis accumsan rhoncus.
Suspendisse commodo, massa eu congue tincidunt, elit mauris pellentesque
orci, cursus tempor odio nisl euismod augue. Aliquam adipiscing nibh ut
odio sodales et pulvinar tortor laoreet. Mauris a accumsan ligula.
Class aptent taciti sociosqu ad litora torquent per conubia nostra, per
inceptos himenaeos. Suspendisse vulputate sem vehicula ipsum varius nec
tempus dui dapibus. Phasellus et est urna, ut auctor erat. Sed tincidunt
odio id odio aliquam mattis. Donec sapien nulla, feugiat eget adipiscing
sit amet, lacinia ut dolor. Phasellus tincidunt, leo a fringilla
consectetur, felis diam aliquam urna, vitae aliquet lectus orci nec
velit. Vivamus dapibus varius blandit.
Duis sit amet magna ante, at sodales diam. Aenean consectetur porta risus
et sagittis. Ut interdum, enim varius pellentesque tincidunt, magna
libero sodales tortor, ut fermentum nunc metus a ante. Vivamus odio leo,
tincidunt eu luctus ut, sollicitudin sit amet metus. Nunc sed orci
lectus. Ut sodales magna sed velit volutpat sit amet pulvinar diam
venenatis.
Albert Einstein discovered that $e=mc^2$ in 1905.
\[ e=\lim_{n \to \infty} \left(1+\frac{1}{n}\right)^n \]
\makeletterclosing
\end{document}
you get the (wished?) result:

.clsfile... Second: Provide a compilable document and specify, which symbols should be removed... – Mar 27 '18 at 11:54\documentclass{...}and ending with\end{document}instead of code snippets. Otherwise we have no way of testing anything. – campa Mar 27 '18 at 12:42