You can merge the grep into the sed like so:
exec 3> >(sed -une '/^good:/s//I got: /p')
echo "bad:data1">&3
echo "good:data2">&3
Unpacking that a bit: You can put a regexp (between slashes as usual) before any sed command, which makes it only be applied to lines that match that regexp. If the first regexp argument to the s command is the empty string (s//whatever/) then it will reuse the last regexp that matched, which in this case is the prefix, so that saves having to repeat yourself. And finally, the -n option tells sed to print only what it is specifically told to print, and the /p suffix on the s command tells it to print the result of the substitution.
The -e option is not strictly necessary but is good style, it just means "the next argument is the sed script, not a filename".
Always put sed scripts in single quotes unless you need to substitute a shell variable in there, and even then I would put everything but the shell variable in single quotes (the shell variable is, of course, double-quoted). You avoid a bunch of backslash-related grief that way.