Answer: It may take another year for your butterfly bush to become completely adjusted to growing in your landscape, so don't be too concerned about a few yellowing leaves. The plant will drop them and replace them with healthy new foliage later in the season.
You can remove the dead blossoms if you like, but I'd remove each one individually because, like lilacs, you'll find two latent buds at the base of the flower. These buds will be the new leaf and flower growth for later in the summer. If you accidentally cut them off, you won't get any more flowers this summer.
Butterfly bushes are normally left unpruned until spring. They start to grow rather late in the season, especially if they have been pruned hard. Butterfly bushes can be pruned several ways. One method is to prune it off close to the ground to renew it if it has become overgrown and gangly, or if the winter has damaged it severely (or even killed it back tot he ground). This will stimulate new growth from the roots and also help to control overall size. In warmer areas, the shrubs can become very large and this pruning method occasionally makes very good sense. Some gardeners prefer to prune away any winter killed branches and then prune lightly just a bit for overall shape and to encourage branching so the plant grows denser. This will result in more flowers, because the blooms form at the branch tips. Other gardeners will prune it back by about half as a compromise to controlling size and keeping it bushy. It's really a matter of personal preference.
Best wishes with your butterfly bush!
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