So it seem that the protective foil at the back of the LCD (that is supposed to be removed prior to installing the new LCD) ripped out an aluminum-like, reflective sheet at the back of the LCD.
That aluminum-like sheet is also connected to the back of the LCD with plastic (located at the edges on the back of the LCD). Without the aluminum-like sheet the back of the LCD is white(ish) in color, when in fact it should be reflective.
To solve this issue (in case you threw away the aluminum-like sheet along with the protective foil in the garbage - like I did) it’s best to remove the aluminum-like sheet from the old, broken LCD that is being replaced. Note that you will probably have to use scissors or a scalpel in order to cut off the sheet from the plastic connecting it to the back of the LCD. After doing that, carefully align the sheet on the back of the new LCD (maybe even using some kind of sticky tape if you think it’s necessary) and then install the new LCD.
The see-through effect should be gone after that.