How do I delete a hard link?

You can delete it with rm as usual: rm NameOfFile. Note that with hard links there is no distinction between "the original file" and "the link to the file": you just have two names for the same file, and deleting just one of the names will not delete the other.

Actually rm doesn't work:

[user@localhost Products]$ rm AZP/
rm: cannot remove `AZP/': Is a directory
[user@localhost Products]$ rm -r AZP/
rm: cannot remove `AZP': Not a directory

What works is unlink AZP.

I have this script to remove redundant hard links. But take care - it is quite dangerous.

#!/bin/bash
clear
echo Reduce redundant hardlinks in the current folder
echo ------------------------------------------------
echo 
echo "  $(basename $0) [-R]"
echo "      -R means recursive"
echo 
read -p "You can break by pressing Ctrl+C"
echo
ask=1
if [ a$1 == "a-R" ]; then  recursive=" -R "; fi

for i in $(ls -i $recursive | awk '{print $1}' | uniq --repeated | sort); 
do 
    echo "Inode with multiple hardlinked files: $i"
    first=1
    for foundfile in $(find . -xdev -inum $i);
    do 
        if [ $first == 1 ]; then
            echo "  preserving the first file:  $foundfile"
            first=0
        else
            echo "  deleting the redundant file:    $foundfile"  
            #rm $foundfile  
        fi
    done 
    if [ $ask == 1 ]; then 
        read -p "Delete all the rest of redundant hardlinks without asking? y/N "
        if [ a${REPLY,,} == "ay" ]; then  ask=0; fi
    fi  
#   read -p "pause for sure"
    echo
done
echo "All redundant hardlins are removed."
echo

If you want to remove only the link and thus keep the original file, you have to use unlink.