If you modify a work by removing from it or making rearrangements, the modifications you have made are based on your ideas which manipulate someone else's expression. Copyright is concerned with expression, not ideas.
The copyright statutes in the United States do not define what "expression" is. If you wanted to assert copyright over something where your only contribution was chopping, rearranging and deleting existing content, you would have convince a judge that it plausibly constitutes an expression, which would probably be difficult.
For one thing, your expression isn't a piece of content whose existence can be demonstrated on its own. You cannot show the judge:
- here is the material I expressed, viewed separately from the combined work in question; and
- here is where that same material appears in the combined work, which should therefore acknowledge me as a copyright holder
The material you expressed, in isolation, is just a blank, a nothing.
The US Copyright Law has a paragraph about derived works, 103.
FistlyFirstly, (a) states that if a derived work is unlawful, then it enjoys no copyright protection. This has implications for open source software, because, by default, a work grants no permissions for making derived works. The permitted ways for making derived works are defined by the specific license. If the license happens to say that the author of a derived version who simply deletes or rearranges lines of code is not permitted to add their name to the copyright notice, then that holds. If the license is violated, then it lapses, leaving that person with no permission to redistribute. Most open source licenses neglect to have such wording, however.
Subparagraph (b) is about lawful derivative works; this is more relevant to the present topic, has this sentence: [t]he copyright in a compilation or derivative work extends only to the material contributed by the author of such work, as distinguished from the preexisting material employed in the work, and does not imply any exclusive right in the preexisting material.
A deletion or rearrangement does not look like "material contributed", which is "distinguished from the preexisting material". All portions of the derived work are material which is preexisting. Concretely speaking, no line of code in the material is one which cannot be found in the original version.
Of course, people will try anything in court, and sometimes there are surprises.