You have to redefine \letterpagemark
in the preamble to get the desired result.
\documentclass{scrartcl}
\usepackage{scrletter}
\usepackage{blindtext}% only for dummy text
\renewcommand*\letterpagemark{%
\usekomafont{pagenumber}{\thepage}}
\begin{document}
\begin{letter}{Max}
\opening{Hello,}
\Blindtext
\closing{Bye}
\end{letter}
\end{document}

Another possibility would be
\let\letterpagemark\pagemark
Then the same output of the page number will be used for the letter part and the other pages of the document. Note that a possible redefinition of \pagemark
must be done before this line.
Explanation:
With KOMA-Script classes \pagemark
serves to output the formatted page number.
While the main KOMA-Script classes (scrartcl
, scrreprt
and scrbook
) define \pagemark
as
\newcommand*{%
\pagemark
}{%
{\usekomafont{pagenumber}{%
\thepage}}}
the KOMA-Script letter class (scrlttr2
) defines \pagemark
as
\newcommand*{%
\pagemark
}{%
{\usekomafont{pagenumber}{%
\pagename\nobreakspace
\thepage}}}
So there will be the prefix \pagename
in the output of the page number in KOMA-Script letters.
If package scrletter
would redefine \pagemark
to add the prefix, the output of the page number on non-letter pages would be changed, too. Therefore package scrletter
defines \letterpagemark
\newcommand*{%
\letterpagemark
}{%
{\usekomafont{pagenumber}{%
\pagename\nobreakspace
\thepage}}}
and uses \let\pagemark\letterpagemark
inside the letter part of the document.