Your pool is fine and you don’t need to add anything. The toxin resides mainly in their skin and outer epidermal layer. It’s not something that will dissolve into pool water and make the water toxic. If any of the toxin did get into the water it will quickly degrade under chlorine and UV exposure.
My dog chased one of those toads too and before I realized what was going on. Thankfully I stopped her from picking it up but she did manage to lick it. She was frothing at the mouth within seconds and clearly distressed. I rushed her into shower where I held her mouth open and flushed it with water. She then spent the night by my bed with plenty of water and soft blankets to sleep on. She was better by the next day but lucky she only got a small dose. Friends of our had a dog that ingested one and they had to have a vet do a stomach pump and then a charcoal treatment to absorb the toxin. Even with all that, their dog nearly suffered liver failure. She was an older dog so her recovery was long and complicated.
Those toads are nasty and if you find them on your property, scoop them up and toss them away hundreds of yards from your home. I have collected them in a bucket in the past and I will drive them down the road a half mile away and toss them out.