Q.Our Liatris Blooms Are Turning Brown On Top. Should That Part Be Removed?
I’m wondering if there is something that I’m doing wrong?

Certified GKH Gardening Expert
Since they bloom from top to bottom on the spike, the fading blooms will start at the top, too. Is that what you are seeing? Otherwise, it could be overwatering. Liatris are drought tolerant and don't need a lot of water.
Once the entire spike fades, you can remove it from the base. However, leave the foliage till it dies back in fall.
https://www.gardeningknowhow.com/ornamental/flowers/liatris/liatris-blazing-star.htm