For the "big three" (the standard classes, KOMA-Script classes and memoir) biblatex tries to interface with the class as much as possible for the formatting of the bibliography heading.
For memoir that means that biblatex responds to \nobibintoc and \bibintoc. So as Ivan said in the comments, you can just say \nobibintoc before the bibliography you want to hide in the ToC. If you do this inside a refsection you won't even have to restore \bibintoc afterwards, because the effect of these commands is local.
\documentclass{memoir}
\usepackage{biblatex}
\addbibresource{biblatex-examples.bib}
\begin{document}
\tableofcontents*
\chapter{A section}
\begin{refsection}
\textcite{sigfridsson} showed that\dots
\nobibintoc
\printbibliography[heading=subbibliography]
\end{refsection}
\chapter{A section}
\begin{refsection}
\textcite{sigfridsson} showed that\dots
\printbibliography[heading=subbibliography]
\end{refsection}
\end{document}

If all or most of your bibliographies are subbibliographys you can save yourself some typing with \DeclarePrintbibliographyDefaults (which was added in biblatex v3.13 from 2019-08-17).
\documentclass{memoir}
\usepackage{biblatex}
\DeclarePrintbibliographyDefaults{heading=subbibliography}
\addbibresource{biblatex-examples.bib}
\begin{document}
\tableofcontents*
\chapter{A section}
\begin{refsection}
\textcite{sigfridsson} showed that\dots
\nobibintoc
\printbibliography
\end{refsection}
\chapter{A section}
\begin{refsection}
\textcite{sigfridsson} showed that\dots
\printbibliography
\end{refsection}
\end{document}
With a standard class heading=subbibliography does not go to the ToC, so you would use heading=subbibliography if you don't want the bibliography to go to the ToC and heading=subbibintoc if you want it in the ToC.
\documentclass{article}
\usepackage{biblatex}
\addbibresource{biblatex-examples.bib}
\begin{document}
\tableofcontents*
\chapter{A section}
\begin{refsection}
\textcite{sigfridsson} showed that\dots
\nobibintoc
\printbibliography[heading=subbibliography]
\end{refsection}
\chapter{A section}
\begin{refsection}
\textcite{sigfridsson} showed that\dots
\printbibliography[heading=subbibintoc]
\end{refsection}
\end{document}
It is always possible to define a new bibliography heading to give you full control over what happens, e.g.
\defbibheading{mybib}[\refname]{%
\section*{#1}}
\nobibintocbefore\printbibliography– Ivan Jan 15 '21 at 19:15