Hi AlpheccaStars, thank you so much for your help. I see...!
I understand now, thanks to you. This "that" is a relative pronoun, and you cannot omit this one (because this is a subject of the relative clause, I guess..).
I would like to ask one additional question, just to make sure. How about the following sentence? Does it sound okay?
Thank you for your reply. I appreciate your advice, too.
When I have to write some English sentences, I want to make them clear, natural, and ... crisp, as much as possible. I need to use all the help I could get here, really.