While it's not against the rules of having a romance in the Justice League Alliance, it is generally frowned upon if the other team members know about it. And eventually, Hal will likely find out Teelara has no time for romance. In which case, Hal will honor her wishes and be respectful.
Hal does do a sort of half smile, "My partner, Jessica, was geeking out over your sword. It uses anti-matter, right? I didn't understand over half of what she said, but she's very impressed with it."
Hal leads her into the holographic training room. He smiles, hoping to surprise her, "Computer, scan and analyze Teelara's sword and re-create it. Use the closest equivalent of anti-matter but with safeties on so neither of us will get hurt." The computer speaks:
Scanning...Process complete. Use when ready.
And a holographic sword appears by Teelara's feet, appearing very much like Teelara's physical one. "Computer, scan my data banks for Teelara's home planet and re-create an appropriate environment."
Then the room around them vanishes, replaced by a holographic representation of Ephemera. Every rock, the dirt, every true, the various smells, etc, are realistically done in all their glory, beauty and ugliness.
Hal's ring flashes with a bright green light, "Ready when you are, Teelara."