Is it a Tea Rose (an Old Garden Rose) OR is it a HYBRID Tea Rose? Where did you buy it? A local nursery? Mail order?

In your climate, I suspect you had a Hybrid Tea Rose. Is the main plant still alive? Or only the thin suckers?

If all that's left is the thin suckers, I suspect they are rootstock, and your rose is dead.

The hybrid tea part is apparently dead. The rootstock plant that survives will bloom next June, but it is not a good rose. I would dig it up and replant. The Knock Out roses are more hardy than the hybrid tea that froze out.

Grandma, it's getting awfully late in the season to plant anything new. For one thing, most nurseries won't have any selection left. For another the rose may not have adequate time to settle in before cold weather comes. Wait until next spring and pick out a rose you love to replace this one with. You can look for something that grows on it's own roots, so you won't have the root stock growing problem, or you can still get a grafted rose but plant that graft a good 4 or 5 inches below the soil to protect it from winter freezing. It still isn't fool proof but it will help for most winters.

Jeri is right. What you probably have is a HYBRID TEA not a TEA rose. They are very different and in your zone 5 a real TEA rose has NO chance of surviving your winters. They are extremely winter tender. But there are many HYBRID TEA roses that can survive a zone 5 winter if planted correctly. My suggestion is to look for some of the older varieties that have stood the test of time. They're still around for many reasons and one of them is that they are hardier then people think they are.