The Compositae family, also known as Asteraceae or the daisy family, is one of the largest families of flowering plants. Many important homeopathic remedies are derived from this family. Let's examine the botanical classification of the given options:
\begin{itemize}
\item \( Arnica montana \) belongs to the family Compositae.
\item \( Bellis perennis \) (Daisy) also belongs to the family Compositae.
\item \( Ledum palustre \) (Marsh Labrador Tea) belongs to the family Ericaceae (the heath or heather family).
\item \( Millifolium \) (Yarrow), often referred to as \( \textit{Achillea millefolium} \), belongs to the family Compositae.
\end{itemize}
Therefore, \( \text{Ledum palustre} \) is the medicine among the given options that does not belong to the Compositae family.