Is placing a mark on the ear of the sacrificial animal, to facilitate identifying it upon receipt, considered among the forbidden mutilations (tabteek)?

The most preferable and best course of action is to refrain from piercing the ear of the sacrificial animal. One can look for another mark to distinguish it, because scholars have explicitly stated the dislike of sacrificing an animal that has a pierced ear, even if it is for branding. However, it is still sufficient according to the majority of scholars, and this prohibition is one of discouragement (tanzīhī), not outright prohibition (taḥrīmī). An animal with a slit ear, a pierced ear, or one from which something has been cut is disliked for sacrifice. This is based on the hadith of Ali, may Allah be pleased with him, that the Prophet, peace and blessings be upon him, commanded them to examine the eyes and ears, and not to sacrifice an animal that is muqābalah (ear cut from the front), nor mudābarah (ear cut from the back), nor kharqāʾ (ear pierced), nor sharqāʾ (ear slit lengthwise).

As for the cutting of the ears of livestock that is prohibited in the Quran, it refers to slitting the ear of a baḥīrah or sāʾibah as a form of offering to idols. This is different from piercing the ear for branding. Some scholars believe that cutting the ears of livestock is absolutely forbidden due to the general wording of the verse.