How to Hide Favorites on Twitterby Aksana Nikolai
In addition to retweeting, you can 'Favorite' tweets that you like. Favorited tweets have a star icon next to them. If you do not want other users to see your Favorites, you can protect your Tweets. When you protect your account, only your approved followers can see your Tweets and Favorites. If you do not want any users, including your followers, to see you Favorites, you can delete them from your account.
Protect Your Tweets
Sign in to your Twitter account and click the Gear icon on your profile page.
Select "Settings" from the drop-down menu to open the "Account" page. Navigate to the "Tweet Privacy" section of the "Account" page.
Click the "Protect My Tweets" check box. When prompted, enter your account password to confirm that you want to protect your Tweets.
Click "Save" to return to your profile page, which now displays a notice that the Protect Tweets setting is active.
Click “Favorites” on your profile page to see tweets you Favorited.
Hover your cursor over the Tweet you want to unfavorite and click the "Favorited" link next to that tweet.
Refresh the page. The tweet you unfavorited no longer appears in the list of Favorites.