at the tl: dregs of tea are just like dregs of orange juice, or dregs of hot choco, or dregs of soda - useless and yucky. It is the stuff that failed to get dissolved by the water (leaves, cola-syrup, cocoa, orange bits) and thus accumulates by gravity at the bottom of the cup. Just like the dregs that float to the top and accumulate there (like milk-skin), though I don't quite believe it is called dregs in that case?
In other words, 'dregs' is a word used to describe the bottom of the barrel, the trash left after you scooped out all the good stuff from a pool (be that a set/pool of humans for your workforce - ie. "dregs of society" - or a set/pool of merchandise where the merchant is running out of stock, and everyone before you already picked out the apples without blemishes). And that is the way hero is using the word here, he is saying that mc is just trash (like how it is used in the phrase "dregs of society").