Historically, the grave character (0x60) was rendered as a left single quote. In LaTeX, this still occurs in some situations. For example, \textasciigrave from the package textcomp is displayed as a quote using latex with Evince as viewer on my machine, however with xdvi it is displayed as grave and with pdflatex and Evince it is also a grave. The choice of htlatex to render a quote is therefore strictly speaking not a bug, but it is a bit of an odd choice given modern conventions.
A solution is to modify htlatex/tex4ht character mappings, but it is probably easier to use an alternative in your LaTeX source that renders as a grave accent in both dvi/pdf and htlatex output. On my system the literal backtick or glyph 18 work well. MWE:
\documentclass{article}
\usepackage{textcomp}
\usepackage{amssymb}
\begin{document}
\begin{enumerate}
\item textcomp grave: \textasciigrave
\item amssymb backprime: $\backprime$
\item escape literal backtick: \`{}
\item math mode backtick: $`$
\item glyph 18: \symbol{18}
\end{enumerate}
\end{document}
which is an unknown unicode glyph? – user3224237 Oct 12 '15 at 13:43