Lualatex function producing trailing characters

That's due to the change from lua 5.2 to lua 5.3.

You can force the number to be an integer e.g. with math.floor:

\documentclass{article}

\directlua{
    function underscore(s)
        s = tostring(math.floor(s+2080))
        tex.print(s)
    end
}

\DeclareRobustCommand{\Binl}[1]{\directlua{underscore([[#1]])}}%

\begin{document}

Use M\Binl{1} or M\Binl{2}

\end{document}  

s = tostring(math.floor(s+2080))