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.
\pagenameto an empty value? – brainchild Jan 04 '21 at 13:46\nobreakspacein the definition of\pagemarkwould shift the page number to the right. – esdd Jan 04 '21 at 13:57scrlttr2. Wouldn't that be clearer/more specific? Of course, one could mention that it is the KOMA-Script letter class too. – Faheem Mitha Feb 28 '22 at 17:51