Just rinse really well and pour it down the drain (helps clean the drain). I personally would wear rubber gloves for protection and I would also use the laundry/garage sink unless you rinse your sink really well. Don't want to chance a tender baby bottom coming into contact with it just to be on the safe side. Unless your plastic pitcher was the restaurant drink variety, your pitcher should be fine.
The reason I mentioned the restaurant drink variety is that everyone of those has developed cracks in them and you don't want fresh lye water leaking all over (don't ask how I know
.