According to Annes own later statement she had heard the police discussing the silencer connected with the gun on the 8th august . A member of the family then told the police they thought JB was not telling the truth about why the silencer and sights were not on the gun. In her own statement she said they discussed the implications of the blood on the silencer as soon as they saw it.
So If her notes were made at the time you would think that yes the find of the silencer with blood and a hair and the fact it was reported to the police would have been significant enough to be noted.
She heard Jeremy tell police that the gun would not fit in the cupboard with the scope and moderator attached. When she told AP he said Jeremy was lying and told police this. The family also brought this up at the meeting with Jones and Jones though neither seemed to care much.
After the silencer was found the others said it would make no sense for Sheila to kill everyone with it then put it away so they saw it as potential evidence. It was collected along with everything else and police notified but at first police just wanted the moderator and made the family keep everything else till September.
Eaton thought the blood on it might be rabbit blood since Jeremy was claiming he shot rabbits the night before. She was not aware that he didn't actually shoot any. At trial on cross Rivlin kept bothering her about such asking why she thought it could be rabbit blood and she said the fact he claimed he shot rabbits with it and she didn't know anything about such guns only shotguns so didn't know what he might do with it that could get rabbit blood on it.
No one ever told her it might have Sheila's blood inside and that finding Sheila's blood inside would prove she can't have committed suicide. That didn't cross her mind or anyone else in the family. She thought it might be rabbit blood and if it was human blood then the value is simply to say it is unlikely she would bother to put it away before killing herself.
In her COLP statement she reiterated that she didn't recognize the true potential the moderator had:

After her testimony is when the lab presented its case and she realized it. She said she didn't even look at it very close up so could not comment on whether it had a scratch or not on it. If she knew it was significant she would have been nosy and looked closely at it with the men but instead she wasn't with them and kept doing her own thing.