In Varieties of Meaning (2004) Ruth Millikan argues for the continuity of natural and conventional signs (say, between smoke that means fire, and "Feuer" that means fire). In her view, we have to assume that conventional signs emerge from natural signs, and that understanding a language is "simply another form of sensory perception of the world", in order to understand how words and mental representations hinge onto the world at all.
The problem here, in Sellarsian, is how to get things into the space of reasons. Sellars, in Empiricism and the Philosophy of Mind (1953), used the phrase "the space of reasons" to describe the inferential character of meanings and concepts: they only exist because they relate to each other, through logical connections, equivalences, mutual exclusions, explaining what mean by them, etc. Davidson builds on this in developing the thesis of "anomalous monism": yes, words and beliefs are entities in the material world, and they are caused by things, but their content is propositional, and the only thing that makes a proposition true is another proposition. In that sense, there is a "nomological slack between the physical and the mental."
Millikan, on the other hand, is a "right-wing Sellarsian" - a label that has also been attached to Paul Churchland, of Eliminative Materialism fame. So she doesn't buy anomalous monism. The lipstick on the cup, to the extent that it says "Carla", can be true or not just as well as a proposition. In support of this, you could point out that writing systems set out as name tags, then became counters, only very slowly developed into full maps of the sentence structure, and only in some writing systems came to map the phonetic structure as well.
However, such an approach gives rise to paradoxes. For example, there is also the mug that Truus (the senior advisor) uses as a mild act of subversion: it contains a cartoon of a fat cat eating cookies while chatting on the phone, feet on the desk. Next to that is the text: "I'M THE BOSS - and don't you forget it!" That mug, by convention, belongs to Truus - so in the same way that cartoon and "I'm the boss" are like writing her name on the cup. But if people took it to mean that Truus is the boss, that would be false - in a way that writing "Truus" on it could not be false, because that is not a sentence, but that "this cup belongs to Truus" would be right.
Is this a full paradox? Not if you assume that these statements operate on different levels of meaning. "I'm the boss" refers to the cat on the cartoon, the cartoon refers to no one in particular (or we may hope so), and as a sign of ownership, it refers to Truus. But if you posits such different levels, can you also safely assume a continuity between them? It seems precisely the kind of case for which Tarski developed Convention T, which forms the basis of Davidson's belief that propositions are only made true by other propositions. For that was developed precisely to avoid the liar's paradox.
Is this pedantic? Yes it's pedantic. But there is quite an important issue at stake here. That issue is who's talking. The competent use of language is a material as well as a rational process: the bulk of it goes on subliminally, the outcome (sound, writing, gesture, mark) is material, and the interpretation and scrutiny of it is largely ex ante: we analyze what it is in a sentence that strikes us as wrong, and "how can I know what I mean until I see what I say?" BUT we are also creative language users that can see through the babble, or babble without caring, or choose our words with care, or say more than we say, or consciously flout the grammar, or cancel implicatures. And without that transparency, we couldn't make sense at all. So we bump into Humpty Dumpty: "The matter is who's in charge: we or the words".
It's not, of course, as if the talking coffee cups will take over as soon as we allow the lipstick on the coffee cup to speak. But we do have to reconsider our language agency if we do. The risk, that some people will like, is that we become the title of the second movement of John Adams' Violin Concerto: Body through which the dreams flows.