“被” means passive, so before that is what verb act on, after that is actor who do the verb action.
一个姑娘被我的钱包检到以后给我送来了。
verb: 捡(this action use hand, different from 检), verb act on 钱包,the actor is 姑娘,so sentence should be:
我的钱包被一个姑娘捡到以后,她给我送来了。
"Object 被 subject + verb"
The sentence you write means that the gril are picked up by a wallet:P
in your order, we should use 把
一个姑娘把我的钱包捡到以后给我送来了。