A few prefatory remarks are in order, since this is a notoriously complex area of early Christian history. The term 'Gnostic' is somewhat messy and ill-defined, and will be taken to embrace a loose collection of non-orthodox groups that can be generally characterised by a) unique scriptures, b) some degree of repudiation or depreciation of the Old Testament and its God ('the Demiurge'), c) their separation from the rising mono-episcopate, d) a relative degree of secrecy attending their rites and practices, and e) various levels of syncretism with paganism, Hermeticism, Platonism and Neoplatonism. Side-stepping the very difficult question of the nature of orthodoxy and how it arises (famously, Bauer held that “heresy is the necessary precondition for orthodoxy”), let's have a look at several dimensions where the relationship between Gnostic and (proto-)'orthodox' groups effected change in christian thought.
In most cases, Gnostics exercised a negative influence on their orthodox counterparts, insofar as Gnosticism was a "heresy by addition" (Turner, p. 118)-- the groups later termed 'Gnostic' could often be characterised by the use of additional books of scripture, additional rites, etc., and this heretical surplus pushed the early church (defined by the mono-episcopate) to set up their own limits. Tertullian, in his assault on (Gnostic) heretics in De resurrection carnis (I.63) refers to their corruption of the biblical text (stilo); their false interpretations (interpretationes), and “they also introduce secrets of the apocrypha (arcana apocryphorum), the inventions of blasphemy.” Irenaeus, also said that Gnostics “boast that they possess more gospels than there really are” (Haer. 3.11.9). The development of a strictly-delineated Christian canon was complex, but the presence of Gnostics and their expansive (and often hugely broad and ridiculous, cf. Oxyrynchus) canon certainly pushed the church to establish a more explicit and limited set of scripture. This negative influence can be seen in the Gnostic use of e.g. the Gospel of John, which led to its relative distrust and disuse in some orthodox circles. It was relatively unused by the orthodox in the 2nd century, and the earliest commentaries on John both come from Gnostics (Ptolomaeus and Heracleon, ca. 160-170). Also, Hahneman notes (p. 102) that "In Rome at the beginning of the third century, the theologian Gaius, who according to Eusebius was an orthodox churchman (HE 2.25.6), rejected John as a work of the heretic Cerinthus”-- Cerinthus a legendary founder of some Gnostic heresy.
To give a brief outline of other points of influence:
The Gnostics pushed the early church to develop a theology that embraced two 'Old' and 'New' Testaments, and it is no accident that the first writer to frame such a distinction was Irenaeus in his attack on Gnostics (Haer. 4.9.1). This, of course, was a response to the typical Gnostic view that the God of the Old Testament was evil, or at best neutral, and that the world of his creation was correspondingly evil; such a view had tremendous implications for Christian theology, which responded in due course, pushing the church to develop arguments against Docetism (the heresy that Christ was purely spiritual, non-material, and thus didn't actually suffer) and refine their ethical teaching against either two prongs of Gnostic taint. Gnostic ethics were either highly libertinistic (for, if matter was all some illusion created by an evil demiurge, what we do with our material bodies has no bearing on our spiritual state), or highly rigoristic and ascetic.
There is, of course, a lot more to be said and I would be happy to expand or add to any of this if you would like.
Sources: G. Hahneman, The Muratorian Fragment and the development of the canon, p. 73-131, 215-218
Jean Daniélou, The Origins of Latin Christianity, pp. 139-188
R.D. Williams, ‘Does it make sense to speak of pre-Nicene Orthodoxy?’ from The Making of Orthodoxy
J.N.D. Kelly, Early Christian Doctrines, Fifth Edition, pp. 29-41, 52-69, 189-207