English speakers often omit the word "that" when speaking. When I was learning Spanish, the subjunctive tense always felt strange to use. "I wish you'd do the dishes" vs "I wish that you'd do the dishes" sort of thing. This is clearly a different case but the same result of skipping the word "that" when it should really be there.
I'm not the one who downvoted you, btw, but these are different cases.
"I wish you'd do the dishes" sounds fine to most native English speakers, except those who are extremely fussy about language. Leaving out "that" in this sentence will sound wrong to most native speakers (though we can easily gloss over it when reading).
As a native speaker fussy about language, leaving out unnecessary "that"s is something I wish far more native speakers would do. I disagree the sentence sounds wrong, of course, and think including a "that" sounds far more wrong, and should only be done to disambiguate, and only if you cannot reword the sentence to resolve the ambiguity without a "that".
"I wish you'd do the dishes" is fine. Far better than "I wish that you'd do the dishes". The "that" is useless. It's contextually clear what you're wishing, with no misunderstanding.
Many "that"s hide poor sentence structure and are a sign of lazy writing/thinking. Take the following:
- I realize now I need a car.
There is some ambiguity about what exactly I mean. I could use "that" to clear things up:
- I realize that now I need a car.
- I realize now that I need a car.
But that helps me spot the problem isn't the lack of "that", it's the "now", and I subtly alter the sentence's meaning based on where I place it:
- I realize I now need a car.
- I realize I need a car now.
- I now realize I need a car.
I should pick the sentence that most clearly communicates my meaning.
The "that" most certainly should not be in the sentence about dishes—and by most certainly, I most certainly mean subjectively most certainly because it's just a damn awful sentence. You've given a great example of why skipping an unnecessary "that" is as important as not omitting "that" where necessary.
While the article's mistake is a result of omitting a necessary "that", this example about dishes is a case of inserting one that is ugly, unnecessary, and actually ruins the sentence flow.
I'm quite sure leaving out "that" in the given sentence is totally fine. I've been taught that you can leave out that, who, and which if the world after "that" is not a verb.
If it is a verb, you can also use participle as suggested by parent (but if you use participle too often with long sentences, the sentence will become hard to understand). When using the participle, you should never use that, who, or which.
It should also be noted that leaving out "that" (if grammatical correct) can sometime sound wrong to native speakers, but that varies from accent and region since there is no standard (at least as far as I know).