When configuring a new Twitter aggregation Term, you're able to 'auto-disable' certain types of tweets.
Navigate to Discover > Create Term. Now select Twitter. When you select either a Hashtag, User or Search a number of tabs will appear.
Under the Term Settings, you'll see the following drop down options:
Using these options, you are able to specify precisely the 'types' of tweets you wish to display.
Note: All content from this term will be ingested and count towards your data cap. Tweets which don't match the criteria you have outlined will simply be disabled by default. You can still access these tweets within the Disabled list.