Cross out words with overlapping to nearby words

You can shorten your lines.

\documentclass{article}\usepackage{xcolor} \usepackage[most]{tcolorbox}

\tikzset{crossout/.style={thick,red,shorten >=-.5cm,shorten <=-.5cm}}

\begin{document}

Of course, presenting this solution would be cheating. And, no, it won't work in all cases, due to strict limitations on the pairs 
\tcbox[tcbox raise base,
breakable,nobeforeafter, enhanced jigsaw, opacityback=0, sharp corners, parbox=false, boxrule=0pt, top=0pt,bottom=0pt,left=0pt,right=0pt, boxsep=0pt, frame hidden, parbox=false, 
  finish={\draw[crossout] (frame.south west)--(frame.north east);\draw[crossout] (frame.south east)--(frame.north west);}]{
  accepted
  }
  by \textbackslash{}line. Your professor surely knows that TeX doesn't draw oblique lines. With the standard package pict2e it's easier and it will work in any case.

\end{document}

An alternative TikZ solution (less elegant than TeXnician's one).

With overlay you can write over something without occupy space.

I've used shift to enlarge the lines (you can use shorten also here, but I haven't used it because TeXnician already did it, hence I would like to show an alternative).

To align TikZ nodes to normal text, see here: TikZ node in normal text.

\documentclass{article}\usepackage{xcolor} \usepackage{tikz}
\newcommand{\mycrossed}[1]{%
    \tikz[remember picture, baseline=(A.base)]{
        \node[inner sep=0pt](A){#1};
        }%
    \tikz[overlay, remember picture]{
        \draw[red, very thick] ([shift={(-.5,.2)}]A.north west) -- ([shift={(.5,-.2)}]A.south east);
        \draw[red, very thick] ([shift={(-.5,-.2)}]A.south west) -- ([shift={(.5,.2)}]A.north east);
        }%
    }
\begin{document}

Of course, presenting this solution would be cheating. And, no, it won't work in all cases, due to strict limitations on the pairs 
\mycrossed{accepted}
  by \textbackslash{}line. Your professor surely knows that TeX doesn't draw oblique lines. With the standard package pict2e it's easier and it will work in any case.
\end{document}