wow,that is a first Lynn got you covered, what i can't get is how that sauce or sink was by the frog.
anyhow stuff happens sometimes.
for future reference, never feed outside the tank, take a frog out only if absolutely necessary and make sure no food items are around
if anything like that happen first thing you need to do is to stay calm!!! whatever you do make sure you do gently without frog flying anywhere. so in case like yours you just get whatever you have close by, spatula, credit card, something thin and not sharp. I rarely use silicone, mostly i use credit card type of things because for frogs i have silicone is not working, too soft. ok, so next you gently cover a frog with one hand to make it stable and then gently open its mouth with the other one using credit card ( etc). chances are if you gently wiggle whatever he tried to grab it will release on his own and you won't need to use anything else.
Lynn got you covered on what you should do now, watch him how is is feeling, if eating/pooping/etc. i would soak him for a few days in regular warm water ( 20 min a day) to make sure whatever might get absorbed is flushed out.