Custom shape shows unwanted extra line

I didn't know that the path has to be filled. So I update my answer as follows:

1. remove -- from the path and
2. pass the option even odd rule if the filling is needed.

Answer updated to add a hole in the fill

\documentclass[border=1cm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw (-4.261,2.617)..controls (2.5,1.5) and (-4.5,-3)..(3.908,-3.118)
      (-4.261,2.617) arc (148.44:321.42:5);
\end{tikzpicture}
%
\begin{tikzpicture}
\draw[red,fill,even odd rule] (-4.261,2.617)..controls (2.5,1.5) and (-4.5,-3)..(3.908,-3.118)
      (-4.261,2.617) arc (148.44:321.42:5) (-2,-2)circle[radius=1];
\end{tikzpicture}
%
\begin{tikzpicture}
\draw[red,fill,even odd rule] (-4.261,2.617)..controls (2.5,1.5) and (-4.5,-3)..(3.908,-3.118)
      (-4.261,2.617) arc (148.44:321.42:5);
\end{tikzpicture}

\end{document}

I saw Phelype's comment and deleted the post. Now I am undeleting it per request. But I will be happy to delete it again. In any case, full credits go to Phelype Oleinik, who was the first to propose a solution.

In fact, I like Phelype's proposal better than "just removing the line". Here is why:

\documentclass{article}
\usepackage{tikz}
\begin{document}
Reversing the arc:
\begin{tikzpicture}
\draw[fill=blue] (-4.261,2.617)..controls (2.5,1.5) and (-4.5,-3)..(3.908,-3.118) 
 arc (321.42:148.44:5);
\end{tikzpicture}

Just removing the line:
\begin{tikzpicture}
\draw[fill=red] (-4.261,2.617)..controls (2.5,1.5) and (-4.5,-3)..(3.908,-3.118)
      (-4.261,2.617) arc (148.44:321.42:5);
\end{tikzpicture}
\end{document}

The blue corresponds to what I would suggest, namely reversing the arc, and the red one "removing the line", which works at the level of the contour but does not yield a continuous path.

And here is a second reason why I like Phelype's method better.

\documentclass[border=1cm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw [line width=1mm,line join=round]
(-4.261,2.617)..controls (2.5,1.5) and (-4.5,-3)..(3.908,-3.118) 
 arc (321.42:148.44:5) -- cycle;
\end{tikzpicture}
%
\begin{tikzpicture}
\draw [line width=1mm,line join=round]
 (-4.261,2.617)..controls (2.5,1.5) and (-4.5,-3)..(3.908,-3.118)
      (-4.261,2.617) arc (148.44:321.42:5);
 \draw[red] (-4.261,2.617) circle[radius=3mm]
 (3.908,-3.118) circle[radius=3mm];   
\end{tikzpicture}
%

\end{document}