There are three different ways to remove the "sponsored links" at the right hand side of a conversation.
1. Upgrade your Gmail
2. Turn on the 'Hide Ads' setting
- Open Mailplane > Preferences and click "Tweak UI" in the toolbar
- Under 'Gmail' turn on 'Hide Ads'
3. Replace ads with contact information
Use the Rapportive plug-in to replace the sponsored links with useful social information (provided by Rapportive.
- Open Preferences > Accounts > Plug-Ins
- Turn on Rapportive