That’s not what an option select is, they just wake up grab.
If you backdash like you said, you can punish with fwd.mp or ex legs/super. You’re right, her backdash pushes her so far that the punishes you get aren’t that good.
The absolute best way to punish it is to do a neutral jump and then air lightning legs with medium kick. If they block it you will be +1 (if you did it low enough) so you can continue pressure. If they throw, then you will hit them in their recovery and can combo to cr.lp, st.mp, cr.mk xx spinning bird kick (or heavy lightning legs).
You can also try to time your jab so that you hit them out of the startup of their throw, which is pretty hard to time and also a bit riskier because you open yourself up to a lot of other things (like if they mash jab, you will get counterhitted).