Reader Question: "That"

Duncan's question:

I have a question for you.

I spotted this sign at my local Petrol Station today: "The carwash cars love".

The sign was advertising their brushless carwash. It hurts me to read it because I desperately would prefer that they wrote it "The carwash that cars love". So my question, as I'm sure you can guess, is whether or not its acceptable to leave out the "that" in that sentence. Please, break the news to me gently if it is acceptable.

My answer:

The "that" is optional, though I agree with Duncan that the sentence is a little awkward.