Yellowing leaves and leaf damage on butterfly bush
Your shrub looks to be in pretty good shape. The lower leaves on these shrubs often get chewed by insects, but this doesn't affect the blooms at the the top. Butterfly bush has very few pest or disease problems that require management. The most common problem is spider mites. They are so tiny that a hand lens needs to be used to clearly see them, or shaking a branch over a white sheet of paper and watching for tiny moving specks can show them.
Spider mites are found on the undersides of leaves and draw out the sap leaving a discolored, yellow or gray mottled appearance.
Your pictures are showing some of this and some chewing damage, which can be caused by a large number of different insects. Keep the shrub roots moist but not soaking. If you did not fertilize the shrub this spring, give a half dose or one-third dose fertilizer now. A fertilizer listed for flowering shrubs is the type you want. Then return to fertilizing in spring only, next season.
Keep any yellowed or severely damaged leaves clipped off leaving the main stem behind. Some insects are attracted to damaged, yellowing leaves. A strong spray of water under the leaves can knock off most of the spider mites. You can use insecticidal soap or an insect spray to manage the chewing insects. However, this can reduce the 'good' insects that help control spider mites. Avoid spraying when bees are active, and avoid spraying any blooms. Spray tops and undersides of leaves.
Here is an article that includes spider mite management, for your reference:
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