What could be a brown line in the back of an already peeled shrimp?
That is the gastrointestinal tract of the shrimp. It is commonly called a vein or sand vein. It is often removed, but this is not required since it is not harmful and is mostly tasteless.
To devein a shrimp you would make a shallow cut from head to tail and then wipe or rinse out the vein under running water.