Although it is not necessary to keep the manifest after it has been submitted to a marketplace, it's highly recommended that you keep them.
Anytime there's an issue with a listing, tracking it's history all the way to the manifest is vital and helpful. And also, they don't take up very much space on the system.
We have an option to create folders for your marketplace manifests. They can be moved into folders or can be archived to keep them separate from your active manifests.
Steps to create a new folder
Step 1: Click on the + Add Folder button
Step 2: Give you manifest folder a name
Step 3: Click the Save button to create the folder
Move your manifests to those folders.
Step 1: Select the manifests you would like to move to a folder
Step 2: Click the Move to Folder button
Step 3: Select Folder from the drop down and click the Apply button
Once again, it is not required to delete manifests, but very highly recommended to keep them in case it is required to investigate the behavior of any SKU / listings.