I think you are reading something that's translated from another language? Because 拜托了 here is not used exactly the way a Chinese would use it.
Usually 拜托了 is a polite thing to say when you trust something to someone, who will do it for you as a favor. Literally it has the meaning of "This thing, which is very important to me, depends on you to be accomplished, and I am grateful for you helping me out."
In more details, depending on the situation it has two subtly different meanings:
1."Please" in English.
2.Use it just to express your trust and gratitude after the other promises to help you.
e.g.:
1. 我不能去接我的孩子回家,能麻烦你帮我接一下吗?拜托了!(Please! the 1st meaning.)
2. A:你能帮我把这封信转交给Jenny吗?
B:当然,没问题!
A:谢谢!拜托了!(the 2nd meaning.)