Files are marked as "from another computer" using NTFS Alternate Data Streams, as James so graciously explained in another question. I also found a nice guide called Introduction to Alternate Data Streams.
You can run commands to read and write ADS data from the Command Prompt:
MORE < "myapp.exe:Zone.Identifier"
(
ECHO [ZoneTransfer]
ECHO ZoneId=4
)>myapp.exe:Zone.Identifier
And from Powershell:
Get-Content -Path .\myapp.exe -Stream Zone.Identifier
Set-Content -Path .\myapp.exe -Stream Zone.Identifier -Value "[ZoneTransfer]`nZoneId=4"
Some browsers also store other metadata there, such as the Referer and Host URLs of a download.
You can read more about zones at About URL Security Zones. The default ones are:
Value Setting
------------------------------
0 My Computer
1 Local Intranet Zone
2 Trusted sites Zone
3 Internet Zone
4 Restricted Sites Zone
You can read about other known ADS names at Known Alternate Stream Names.