In these examples, "this" versus "that" have a very similar meaning. For all practical purposes, they are identical.
Of course, the word "this" refers to something close by, and "that" refers to something further away. Because of this, the choice of words lends a different flavor to the phrases. The difference is quite subtle. "This" refers to an idea or thought which maybe you feel closer to. "That" refers to something which is more impersonal or general. For example, who cares about dish detergent? It's not important. Let's use "that". I'd say "Because of that".
Next, what about the distinction between "because of" and "due to". Again they have very similar meanings.
"Because of" is more common, simple, idiomatic, and conversational. "Due to" sounds more literate or scientific.
Because cleaning a table is a common everyday task you should probably use "because". If you were writing a newspaper article or a novel, then "due to" could be an appropriate choice.
(US English. Perhaps UK English differs.)