Thanks for writing. I'm not aware of any home remedies that actually work that you can use on petunias to control budworms. Any kind of product -- homemade or not -- can be tough because the insects crawl into the flower buds and most products don't penetrate into the flower buds.
To help deter them next year, you can till up the area this fall. The budworms overwinter in the soil, so fall tilling will disrupt their life cycle. You can also spray a natural insecticide called Bt in spring when the budworms crawl out of the soil and begin attacking plants.
---Justin, Senior Garden Editor, BHG.com