tar -ztf file.tar.gz | while read FILENAME
do
        if tar -zxf file.tar.gz "$FILENAME" -O | grep "string" > /dev/null
        then
                echo "$FILENAME contains string"
        fi
done

zgrep -a string file.tar.gz

$ tar xf file.tar.gz --to-command "awk '/bar/ { print ENVIRON["TAR_FILENAME"]; exit }'"
bfe2/.bferc
bfe2/CHANGELOG
bfe2/README.bferc

tar zxf file.tar.gz
for f in hopefullySomeSubdir/*; do
  grep -l "string" $f
done

tar xzf example.tgz --to-command 'grep --label="$TAR_FILENAME" -H PATTERN ; true'

targrep () {
    for i in $(tar -tzf "$1"); do
        results=$(tar -Oxzf "$1" "$i" | grep --label="$i" -H "$2")
        echo "$results"
    done
}

targrep example.tar.gz "pattern"

tar -ztf file.tar.gz | while read FILENAME
do
        (if tar -zxf file.tar.gz "$FILENAME" -O | grep -l "string"
        then
                echo "$FILENAME contains string"
        fi) &
done

local tempPath=`tempfile`
mkdir $tempPath && tar -zxf file.tar.gz -C $tempPath &&
find $tempPath -type f | while read FILENAME
do
        (if grep -l "string" "$FILENAME"
        then
                echo "$FILENAME contains string"
        fi) &
done && rm -r $tempPath

-l, --files-with-matches
          Suppress normal output; instead print the name of each input file from which output would
          normally have been printed.  The scanning will stop on the first match.  (-l is specified
          by POSIX.)

pattern=$1
for f in *.tar.gz; do
     echo "$f:"
     tar -xzf "$f" --to-command 'grep --label="`basename $TAR_FILENAME`" -Hin '"$pattern ; true";
done

tar -xzf "$f" --to-command 'echo "f:`basename $TAR_FILENAME` s:'"$pattern""

'grep --label="`basename $TAR_FILENAME`" -Hin '"$pattern ; true"