You could use variable substitution:
$ OUTPUT=a\'b\"c\`d
$ echo "$OUTPUT"
a'b"c`d
Use that syntax: ${parameter//pattern/string} to replace all occurrences of the pattern with the string.
$ echo "${OUTPUT//\'/x}"
axb"c`d
$ echo "${OUTPUT//\"/x}"
a'bxc`d
$ echo "${OUTPUT//\`/x}"
a'b"cxd
$ echo "${OUTPUT//[\'\"\`]/x}"
axbxcxd
