subordinate clauses - Use of the phrase "it seems" vs. "it seems that"

On another stackexchange site, I used the following phrasing:

I want to do X. It seems I can only do so when Y.

Someone edited the second sentence:

It seems that I can only do so when Y.

This made me realise that the edited form is perhaps more common -- but is my original phrasing grammatically incorrect? What role does "that" play in the second variation?