Hello, Edward!

As redbud trees age they often shed their bark. As the trees grow, the bark layer thickens and the outermost tissue eventually dies. On older redubuds, when the outer bark on the trunk falls off, the orangish-grown inner bark is revealed. Dry conditions in summer and fall and cold winter conditions may loosen more bark than normal. As long as the tree continues to appear healthy, there is no cause for concern.

https://www.canr.msu.edu/news/bark-shedding-from-trees-during-summer

Continue to keep the tree as healthy as possible by fertilizing in spring after it flowers, watering in dry periods, and mulching around the root area. Keep an eye on the the crossing branches where they originate on the trunk. It is an area that may be vulnerable to splitting or cracking as the tree ages.

Enjoy those beautiful redbud flowers!