Actually, submodifier is an entry in the book, as is sentence adverb, a label that other dictionaries would do well to consider.
The books give similar advice at disinterested, as they do at the fading feminine ending -ess, and their notes about the use of hopefully as a sentence adverb supplement each other.
Consider the following sentences from German (the sentence adverb is put in italics):
They must scramble to the left of the sentence adverb to be destressed and get the required anaphoric reading.
In (40) the assumed licensing requirement of the AF-feature is disrespected, as the direct object stays to the right of the sentence adverb, that is in situ, according to our assumptions.
The tacit premise for this analysis has been twofold: (a) an assumed basic sisterhood relation between argument and verb for the purposes of case and theta marking, credited mostly to Chomsky (1965), but in its essence going back at least to the Port Royal Grammarians, and (b) an idea of Pollock (1989) that sentence adverbs have a fixed attachment site (in [1a] and [1b] the maximal projection of V) in the sentence structure.
Even if de Hoop's (1992) analysis strikes one as a sophisticated reformulation of the problem on a more abstract level, (5) the basic insight remains valid: the position of the direct object to the left or right of sentence adverbs corresponds to the semantic domains of generic and existential binding.
Note that focus projection is blocked if the direct object is to the right of sentence adverbs, that is in its base position, where it is assigned contrastive stress: