Why is sed not recognizing \t as a tab?

Question

sed \"s/\\(.*\\)/\\t\\1/\" $filename > $sedTmpFile && mv $sedTmpFile $filename

I am expecting this sed script to insert a <

Answer 1

TAB=$(printf '\t')
sed "s/${TAB}//g" input_file

It works for me on Red Hat, which will remove tabs from the input file.