Along with being able to view or modify that data, users can request a list of advertisers that have targeted them. You just have to click the "Request advertiser list" button under the Your Twitter Data settings, and almost instantly you will receive a PDF of the Twitter handles of companies that dangled their sweet promotions in your feed. Mine was 69 pages of Twitter handles, including @randpaul, @realdonaldtrump, @hillaryclinton, @airbnb, @comcast and @twitter.
Tweaking the data advertisers are able to see will have a direct impact on the types of ads you'll find in your feed, but as Twitter notes in Settings, "it won't remove you from advertisers' audiences." Simply put, while you can try and manage the thousands of advertisers looking to lure you in (according to my profile, I'm a part of 19,831 audiences from 4,019 advertisers), you can't hide from them.