Nasal Mucus (مخاط) is considered ritually clean, it will not invalidate Salah if it is present on your body or clothing. From Mawsoo‘ah al-Fiqhiyyah 36/258:
Mucus is defined as that which flows from the nose just like saliva flows from the mouth ...
The jurists agree that mucus is ritually clean, and Salah is correct if it is offered in a cloth which is soiled with mucus.
This is derived from the hadith:
"If one of you must spit, then let him spit to his left, beneath his foot. If he cannot do that, then let him do like this," and Al-Qasim described how he spat into his garment then rubbed part of it against another part."
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