I doubt it'll just flush out...
Depending on what the sauce was made of, you'll want some H202 for the natural colours from the tomato, but you may need a redecing agent for artifical colouring.
I'd flush out with a good wool safe/approved detergent, maybe add a tad of heat from a steamer and flush well.
Do two small test areas, one with H202 and the other with a reducing agent. (sorry I'm not familiar with SMFW)
Neutralise and flush out both and then use the best result one for the remainder of the stain. It may require a couple of treatments, or the use of the steamer, or even both treatments, BUT I'd advise against doing both chemicals on the same day. Re book for the next day. You'll run the risk of chemical reactions. I remember one job years back where I hadn't sufficinetly neutralised the H202 before applying the reducing agent and the carpet started smoking, while a white vapour anyway... not good, one of my few heart racing moments.
If it's WHITE wool, be prepared you may not get it all. Depends natuarally on age, condition, wear, soiling etc, not to mention what the client has already thrown at it.
Careful of too much aggression, you'll leave a felted fuzzy mess that the client won't like even if you get the stain out. Use duck bills to carefully de pill it.
John