ファイル名セットからn番目の文字を削除する方法は？

使用している機能に関するマニュアルページを引用することをお勧めします。次のEXPANSIONセクションではman bash：

${parameter:offset:length}
       Substring  Expansion.  Expands to up to length characters of the value of parameter starting at the character specified by offset.  If parameter is @, an 
       indexed array subscripted by @ or *, or an associative array name, the results differ as described below.  If length is omitted, expands to the substring
       of  the value of parameter starting at the character specified by offset and extending to the end of the value.  length and offset are arithmetic expres‐
       sions (see ARITHMETIC EVALUATION below).

       If offset evaluates to a number less than zero, the value is used as an offset in characters from the end of the value of parameter.  If length evaluates
       to  a  number less than zero, it is interpreted as an offset in characters from the end of the value of parameter rather than a number of characters, and
       the expansion is the characters between offset and that result.  Note that a negative offset must be separated from the colon by at least  one  space  to 
       avoid being confused with the :- expansion.

内部的に算術演算を実行できるため、${}次のようにコードをパラメータ化できます。

#!/bin/bash
position=5

for f in *JPG; do
   mv -- "$f" "${f:0:$position-1}${f:$position}"
done

exit

ここに迅速かつ汚れた解決策があります。ファイル名の長さやその他はチェックしませんが、このようなハッカーには問題ありません。