The title asks how to understand Trim_Galore --trim1 parameter, but apparently the real question is "why alignment is invalid if a start/end coordinate is contained within the other read?"

I don't know why bowtie considers an alignment invalid if a start/end coordinates is contained within the other read start/end coordinates. It could be a design decision (this would be my guess, probably to avoid funky reads - read more bellow), or it could be some limitation impose by Bowtie algorithm. The fact is bowtie manual clearly states this:

Paired-end alignments where one mate's alignment is entirely contained within the other's are considered invalid.

edit: bowtie source code comments at the file aligner.h hints it is a design decision:

    // Set begin/end to be a range of all reference
    // positions that are legally permitted to be involved in
    // the alignment of the outstanding mate.
    //
    // Note that one of the constraints imposed on which positions
    // go into this range is that the opposite mate cannot be
    // contained entirely within the anchor mate, or vice versa.

and:

        // We can also add a bit more if qlen is less than alen,
        // since we're requiring that opposite not be contained
        // within anchor.