I want a backquote "`" to appear in my bibliography, and not an opening single quote "‘". (I am referring to a Mathematica package.) To properly produce this in TeX, you need to do \textasciigrave. But Biber doesn't preserve this in its output: the \textasciigrave turns into ` in the .bbl file, which TeX then turns into an opening single quote.

Here is the relevant entry in the .bib file:

@misc{QuantumGroups,
	Author = {Scott Morrison},
	Title = {\texttt{QuantumGroups\textasciigrave}, a Mathematica package},
	Year = {2006}}

and the resulting output in the .bbl file includes:

      \field{title}{\texttt{QuantumGroups`}, a Mathematica package}

Oddly this doesn't happen with everything, eg \textbackslash does not turn into a literal backslash in the output.

This is with Biber version 2.18 on Debian unstable; apologies that I wasn't able to compile the latest version from GitHub to check that. (Debian does not package Mozilla::CA.) Full minimal example below.

File t.tex:

\documentclass{amsart}
\usepackage[backend=biber,style=alphabetic,doi=false,isbn=false,url=false,minnames=6,maxnames=6]{biblatex}
\addbibresource{t.bib}

\begin{document}
Test citation of \texttt{QuantumGroups\textasciigrave} \cite{QuantumGroups}
\printbibliography
\end{document}

File t.bib:

@misc{QuantumGroups,
	Author = {Scott Morrison},
	Note = {\url{http://katlas.org/wiki/QuantumGroups\textasciigrave}},
	Title = {\texttt{QuantumGroups\textasciigrave}, a Mathematica package},
	Year = {2006}}

PDF output attached.
t.pdf