I was watching Sora no Method 06, and at about 17:03 the line 今日は誘ってくれて嬉しかった came up. Crunchyroll translated the line as "I'm happy you invited me today," but the problem is that she was invited the day before, not today, but Crunchyroll's line made it seem like she was invited today. Is it possible that 今日 only modifies 嬉しかった and doesn't necessarily specify the day that 誘う happened?
今日は誘ってくれて嬉しかった sounds perfectly natural to me. I think it's like "Thank you for asking me out for today." implying "Today, I had a great time."
今日誘ってくれて嬉しかった sounds to me like "I was happy you asked me out TODAY, not another day."
That 今日 indicates the day when she felt happy. If it's the day when she was invited (for), the sentence would be 今日誘ってくれて嬉しかった.