sed/awk to remove double quotes " that are inside of curly braces {}

It would be easier with sed:

sed -e :1 -e 's/\({[^}]*\)"\([^}]*}\)/\1\2/g; t1'

Or perl:

perl -pe 's{\{.*?\}}{$& =~ s/"//gr}ge'

Note that it assumes there's no nested {...}.

To handle nested {...}, you can use perl's recursive regexp capabilities:

perl -pe 's(\{(?:[^{}]++|(?0))*\})($& =~ s/"//gr)ge'

With sed, working our way outwards to escape the inner {...}s before removing the "s:

sed 's/_/_u/g
     :1
     s/\({[^{}]*\){\([^{}]*\)}/\1_<\2_>/g; t1
     :2
     s/\({[^}]*\)"\([^}]*}\)/\1\2/g; t2
     s/_</{/g; s/_>/}/g;s/_u/_/g'

Related