This is very basic.
Sentences with propositional content (like " it's raining") are claims regarding truths about reality. Hence they are truth-claims. Not all sentences are such (eg. "Let us go to the movies" is a request and can't be said to be either true or false).
Non of the above represents science. scientific hypothesis nor theories make claims that something is true nor false,
Science is in the business of gathering evidence for or against various truth claims about the world.Actually, theories and hypothesis cannot propose to falsify the negative nor against anything. They can only falsify positive proposals for theories and hypothesis.
Disagree all you like, but science is a method of knowing (epistemology)precisely because it does this evaluation through the scientific method.
All propositional statements have truth value. See below
Truth Values (Stanford Encyclopedia of Philosophy)
No references in the Stanford Encyclopedia describe science making 'Truth claims. In fact other reference describe 'Truth Claims' as 'belief system claims' (wikipedia) and others consider it controversial as far as science is concerned.
Excellent reference here on the concept of 'Truth Values' in different contexts, but nothing here reflects your claim that science makes 'Truth Claims.' It is best from the scientific view versus theological/philosophical truth is to look up the correspondence theory of truth versus the coherent theory of truth. Among these references it discusses a hybrid theory of truth I like, but I do not remember exactly where.