can we deny an invite back?

Yes, if you don't go you run the risk of not getting a bid. Also lots of girls pledge houses they didn't love the first day so it's good to see some houses the second time around.

Yep if you don't go it looks extremely bad. Like really really really bad. Keep in mind girls in different sororities live together/are best friends. It would get around and other sororities could drop you for it. it's just straight rude.

Not going back would be considered not maximizing your options which means that you would not be elligible for quota additions--aka you won't be guaranteed a bid even if you have 3 houses on pref.

If you don't want to be invited back to a house then just don't list them on your ranking card after the first round. It's that simple. But I would advise you to list everyone because you never know if you might fall in love with a house at the next party.

It's possible. This isn't prison. But on the other hand, it's not advisable.

For one thing you don't have any idea after that short of a time whether or not you will eventually have a connection there.

For another thing, the only way you would get that sorority (assuming you ranked it low) was because some of the houses you liked better didn't invite you back. This is a mutual selection process and you have no guarantees.

Your question itself suggests a certain amount of entitlement. It suggests that you may feel you are too good for certain houses based on gossip and rumor. Houses are not interested in girls with this kind of attitude. No one would want to live in a house with 200 or so girls like that. Right?!

Suggestion: Get off greek rank and work on your social skills so girls will actually want to be your sister.

How can you know after 15 minutes? Girls change their minds about groups from day to day. You might not have connected today, but you might get someone else the next day that you click with.
You're there.
Go and give it a try.

Also, you don't cut groups. You rank them. And it's entirely possible to rank a group as low as possible and see them on your party list for the next day. It's because the other groups did not invite you back.