Praise be to Allah
What appears to be the case is that this layer of blood that forms over the wound comes under the same ruling as skin, because it is attached to the body, and removing it is harmful.
So it is sufficient to wash its outer surface, and you do not have to remove it.
An-Nawawi (may Allah have mercy on him) said in al-Majmoo‘ (2/232):
Abu’l-Layth al-Hanafi said in his Nawaazil: If someone has an ulcer and it becomes raised, and its surface becomes raised, and the edges of the ulcer are attached to the skin, except the part from which pus comes out, so it is raised and the water cannot reach what is beneath its outer layer, then his wudoo’ is valid. End quote.
In Haashiyat al-Bujayrami ‘ala al-Khateeb (1/128), it says: al-Qaffaal said: Accumulation of dirt on a part of the body does not cancel out the validity of wudoo’ and it does not have to be removed if it has become a part of the body, because it is not possible to separate it from it. What is meant by its having become like a part of the body is if it cannot be distinguished from the body in the eye of the beholder. End quote.
If the dirt has become attached to the body to the extent that it has become a part of it, it does not have to be removed, so it is more appropriate that the layer covering a wound should not be removed than in the case of dirt.
And Allah knows best.