Same situation here. Was running MacOS 10.13.5 - have now updated to 10.13.6 and so far it appears solved.
Suspect a false positive.My Process:Got lots of quarantine messages for the same 'MacOS:Genieo-FM MRT [Adw]' filename mentioned in other posts here, located in /System/Library/CoreServices/MRT.app/Contents/MacOS/MRT. Clicked the messages away and they popped up again, probably about 3-4 messages a minute. Frustratingly spammy!
I looked up the named file and learnt about Genieo - apparently it's adware. Didn't download any uninstaller for it as apparently these can add even more adware. Checking the Mac and browsers I couldn't find the application, and both Safari and Firefox had no extensions running. My search only led me to the MRT folder, which I didn't click on or attempt to explore further.
Phoned Apple for support. They got me to check safari for extensions again (nothing there, as mentioned), then recommended I download Malwarebytes and run a scan.
(Regarding Malwarebytes quickly - It is free and legit and fine. I saw it recommended elsewhere when searching for solutions, but when I first entered the site it automatically started downloading so had assumed it was some more dodgy malware and ran a mile! This isn't the case, and the Apple support chap said it was the only third party software they recommend for problems like this. You just go to the download now button which gives you a free 30 day trial. I'm think I'm going to wait till it runs out before deleting it - might come in handy if the problem comes back before then!) Malwarebytes scan showed all clear. We restarted the Mac and scanned again. Still all clear.
Apple chap recommended I update the MacOS from 10.13.5 to 10.13.6, as the system has its own security processes built in that might be able to clear up whatever it was.
My Solution:Updated the OS around 4.30 pm, computer restarted - got 2 more quarantine notifications that appeared to have been before the restart (4.25), and have had none since (it is now 5.45 - or 6.45 according to the forum times here) so all clear for about an hour. Fingers crossed it's been solved. Will update if it comes back!
The Apple support chap discussed the possibility of it being a false positive, and was going to recommend that I get in contact with Avast if it didn't sort itself out. It seems like I haven't needed that stage.
My Conclusion:The apparent lack of visible Genio anywhere on my system, and the explicit details in the filename (see below) lead me to suspect that Avast has mistaken the Mac's own security system's definition of the adware as the adware itself.
The file name I encountered: 'MacOS:Genieo-FM MRT [Adw]' is short, highly structured and very explicit in describing a Mac operating system, the name of the adware, 'FM' (possible firmware?) , 'MRT' (name of Mac's Malware Removal Tool) and '[Adw]' - presumably an added note/detail to classify Genio as Adware (Adw). It strikes me as a name used to classify a virus, rather than the name of a virus itself. Most virus names (in my experience) are either slightly fake-sounding app names or seemingly random combinations of letters and numbers.
That's my tuppence, hopefully this has been helpful!
(I notice that the OP posted this at 2.54pm and the clock in the screenshot says 1.35pm. My first quarantined message was at 2.30pm exactly (GMT-0 + British Summer Time, I'm in the UK - apparently 1 hour behind the time listed in this forum). When did everyone else start getting the messages? Might help work out if it's an Avast/false-positive thing that might have happened when some definitions changed.) Michael1519's message about an Avast update would seem to support the likelihood of a false positive I too am having this same problem. I tried to delete the files in Virus Chest but they continue to reappear as well as the pop ups. Online solutions didn't work because the Genieo app does not exist on my Mac. It appears from all the other comments here today as well as the fact that Avast updated the Mac version to 13.9 that it is likely a glitch in the latest AVAST release.