Need tall QED symbol

Here, I just scaled the \square in the vertical direction by a factor of 1.5 times the width, and called it \tallqed. The \smash prevents it from affecting line spacing. EDITED to reduce size. Note that first argument of \scalebox is the horizontal scaling, while 2nd (optional) argument is the vertical scaling. These can be adjusted to suit.

\documentclass{article}
\usepackage{amssymb,graphicx}
\def\tallqed{\smash{\scalebox{.75}[1.125]{$\square$}}}
\begin{document}

\noindent In view of the choice we made for the orientation of $\partial D$, we conclude that 
\[\int_{\partial \mathbf{D}} \iota^*\omega = 
(-1)^n \int_{\mathbb{R}^{n-1}} a_n(\cdot,\cdot, \dots, \cdot, 0).\]
This completes the proof of the theorem. \tallqed
\end{document}

WChargin correctly points out that the symbol stretch makes the box border thickness non-uniform on the sides compared with the top/bottom. If that is an issue, the problem can be remedied with a slightly altered definition, by \ooaligning two of the stretched \squares with a slight kern.

\documentclass{article}
\usepackage{amssymb,graphicx}
\def\tallqedX{\smash{\scalebox{.75}[1.125]{$\square$}}}
\def\tallqed{\ooalign{\tallqedX\cr\kern.2pt\tallqedX}}
\begin{document}

\noindent In view of the choice we made for the orientation of $\partial D$, we conclude that 
\[\int_{\partial \mathbf{D}} \iota^*\omega = 
(-1)^n \int_{\mathbb{R}^{n-1}} a_n(\cdot,\cdot, \dots, \cdot, 0).\]
This completes the proof of the theorem. \tallqed
\end{document}

I'd use amsthm and its automatic \qed feature. But if you want, you can use \tallopenbox by itself.

\documentclass{article}
\usepackage{amssymb,amsthm}

\newcommand{\tallopenbox}{\leavevmode
  \hbox to.4em{%
  \hfil\vrule
  \vbox to.8em{\hrule width.3em\vfil\hrule}%
  \vrule\hfil}}
\renewcommand{\qedsymbol}{\tallopenbox}


\begin{document}

\begin{proof}
In view of the choice we made for the orientation of $\partial D$, we conclude that
\[
\int_{\partial \mathbf{D}} \iota^*\omega =
(-1)^n \int_{\mathbb{R}^{n-1}} a_n(\cdot,\cdot, \dots, \cdot, 0).
\]
This completes the proof of the theorem.
\end{proof}

\end{document}

Modify the height (here 0.8em) and the width (here 0.4em); the inner width (here .3em) should a little smaller than the outer width.

As a simple alternative to scaling the \square, consider employing a \framebox with a \phantom symbol:

\def\tallqed{\setlength{\fboxsep}{-\fboxrule}\framebox{\phantom{t}}}

You could customize the box thickness by adding, e.g., \setlength{\fboxrule}{.3pt} or pick another phantom symbol for adjusting the box size.