The more common term is deflationary theory of truth, where "assertions of predicate truth of a statement do not attribute a property called "truth" to such a statement".
I did not find reference to conditionals and disjunctives specifically in Baldwin's essay in Frege: Sense and Reference One Hundred Years Later, but Frege's own example of a conditional is:
"In the formula '(2 > 3) ⊃ (7^2 = 0)' a sense of strangeness is at first felt, due to the unusual usage of the signs '>' and '='. For usually such a sign serves two distinct purposes: on the one hand it is meant to designate a relation, while on the other hand it is meant to assert the holding of this relation between certain objects. Accordingly it looks as though something false (2 > 3, 7^2 = 0) is being asserted in that formula - which is not the case at all. That is to say, we must deprive the relational sign of the assertive force with which it has been unintentionally invested". [quoted from Greimann]
So if phrased as "if it is true that 2 > 3 then it is true that 7^2 = 0" the 'true' has no assertoric force. The same happens with disjunctives phrased as "it is true that the Riemann hypothesis holds or it is true that it does not" since the truth can not possibly be asserted of both disjuncts.
Frege goes on to distinguish two distinct functions that the copula ("is") and relation symbols serve in natural languages, predication and assertion. Only the first function is retained in conditionals and disjunctives. Under the redundancy/deflation conception of truth the 'true' adds nothing to the thought, but it can not add the assertoric force in conditionals and disjunctives either. So the surface grammar of declarative sentences in natural languages conflates expressing the content to be judged true or false with asserting that it is true. Hence, in the "scientific language" the functions of predication and assertion must be separated, according to Frege. Greimann gives a good discussion in The Judgement-Stroke as a Truth-Operator.
As for the assertoric force, Frege himself acknowledges that it is lacking even in purely assertive sentences, when uttered, e.g., by actors on a stage, but still believes that it is somehow intended:
"The truth claim arises in each case from the form of the declarative sentence, and when the latter lacks its usual force, e.g. in the mouth of an actor upon the stage, even the sentence 'The thought that 5 is a prime number is true' contains only a thought, and indeed the same thought as the simple '5 is a prime number'. [...] So the word 'true' seems to make the impossible possible: it allows what corresponds to the assertoric force to assume the form of a contribution to the thought. And although this attempt miscarries, or rather through the fact that it miscarries, it indicates what is characteristic of logic... 'True' makes only an abortive attempt to indicate the essence of logic, since what logic is really concerned with is not contained in the word 'true' at all but in the assertoric force with which a sentence is uttered." [quoted from Baldwin]
Baldwin characterizes this explanation as a "mess". Dummett proposes a modal reading of it:"the root notion of truth is then that a sentence is true just in case, if uttered assertorically, it would have served to make a correct assertion". This is better, but the trouble is that an assertoric utterance depends on the sense of the asserted sentence, and, on Frege's account, this sense is given by... the sentence's truth-conditions. So "the root notion of truth" derives... from the truth itself. In short, Frege's attempt to add something extra to the bare deflationary function of 'true' itself miscarries.