You can export comments of an asset and import them into Avid Media Composer with the following simple steps.
Export your comments for Avid Media Composer from the comment export menu. This will download an Avid Marker XML file.
Before you can import the downloaded Marker XML file, make sure that you have the target sequence open.
Next, open the Marker window in Media Composer. Therefore choose Tools > Markers from the app's menu.
Right click in the Markers panel and choose Import Markers.
From the file picker dialog make sure you have the Text/XML option selected. Then select the XML file and click Open.
The blue markers are timebased comments. General comments are magenta and have been added to the TC1 track. If you double click a marker, the playhead will jump to the appropriate frame.
Note: if you don't see the marker text overlaid in your sequence monitor then right-click and choose Show Composer Markers and make sure everything is checked.