Some Muslims wipe over their shoes while wearing socks [underneath] for example, then remove the shoes before entering the Masjid and pray with their socks, believing that this method of wiping in Wudhoo is correct, Is this correct?

No it isn’t correct! Wiping must be over the socks. If a person wipes over his/her shoes while wearing socks, then removes the shoes, the Wudhoo is consequently finished, it is nullified! Because if he/she wipes over both of them together [i.e. wipes over the shoes while wearing socks] then the Wudhoo is nullified by removing either one of them.

However, if a person wipes over the socks, then wears shoes or sandals, then there is no harm if he removes [the shoes or sandals] because the ruling is over the socks. So if the shoes or sandals are removed there is no harm in this case.

If the person wipes over them both, then the ruling is tied to them both, if either of them is removed the Wudhoo is nullified.