Hello,
This is probably transplant stress.  I recommend pruning the dead twig so that another leader can develop to take its place.  The shape of this arborvitae might always be a little more boxy than the rest due to this, but it is best to remove the dead growth.  I would also pull the mulch away from the trunk of the tree and make sure the mulch is only a few inches deep, as you can encourage root problems otherwise. It might be a good idea to check the other transplants and do this for them, as well.  The mulch can extend a bit further out so that lawn equipment can have a wide margin for mowing.

 For future reference, it is best to hold off on fertilizing transplants until the tree is more established.  When transplanting trees, no matter how careful you are, a great deal of root loss and damage occurs.  Fertilizer can burn roots of young seedlings and cause scorching not unlike what you are seeing on this seedling.  Make sure to water frequently with new transplants, but don't overdo it.  The soil should feel like a wrung-out sponge most of the time- arborvitae like moist, well-drained soil.  Here is more information about arborvitae: https://extension.psu.edu/the-mighty-arborvitae

I hope this is helpful!
Thank you for contacting Ask Extension.
Ruth

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