Metanoia is very clearly defined in Greek literature and also how it used in scripture.
It literally means to to turn away from towards something new ... also sometimes stated as a change of mind.
You should also take note that according to the original language of Koinee Greek, which is a gendered language .... the gift is salvation and faith is not part of the gift because the gender does not agree.
From Baker’s New Testament Commentary
A. T. Robertson. Commenting on this passage in his
Word Pictures in the New Testament, Vol. IV, p. 525, he states, “Grace is God's part, faith ours.” He adds that since in the original the demonstrative “this” (and
this not of yourselves) is neuter and does not correspond with the gender of the word “faith,” which is feminine, it does not refer to the latter “but to the act of being saved by grace conditioned on faith on our part.” Even more clearly in A. T. Robertson,
Grammar of the Greek New Testament in the Light of Historical Research, p. 704, he states categorically, “In Eph_2:8 … there is no reference to διὰ πίστεως [
through faith] in τοῦτο [this], but rather to the idea of salvation in the clause before.”
Without any hesitancy I answer, Robertson, to whom the entire world of New Testament scholarship is heavily indebted, does not express himself felicitously in this instance. This is true first because in a context in which the apostle places such tremendous stress on the fact that from start to finish man owes his salvation to God, to him alone, it would have been very strange, indeed, for him to say, “Grace is God's part, faith ours.” True though it be that both the responsibility of believing and also its activity are ours, for God does not believe for us, nevertheless, in the present context (verses Eph_2:5-10) one rather expects emphasis on the fact that both in its initiation and in its continuation, faith is entirely dependent on God, and so is our complete salvation. Also,
Robertson, a grammarian famous in his field, knew that in the original the demonstrative (this), though neuter, by no means always corresponds in gender with its antecedent. That he knew this is shown by the fact that on the indicated page of his Grammar (p. 704) he points out that “in general” the demonstrative “agrees with its substantive in gender and number.” When he says “in general,” he must mean, “not always but most of the time.” Hence, he should have considered more seriously the possibility that, in view of the context, the exception to the rule, an exception by no means rare, applies here. He should have made allowance for it. Finally, he should have justified the departure from the rule that unless there is a compelling reason to do otherwise the antecedent should be looked for in the immediate vicinity of the pronoun or adjective that refers to it.
From the Cambridge Bible for Schools and Colleges, on Eph. 2:8
The question is largely occasioned by the construction of the Greek, in which “
that” (neuter) does not agree with “
faith” (feminine).—
Many great expositors, Calvin at the head of them, accordingly take “that” to refer to the main previous idea, and “through faith” to be a separate inserted thought. Alford, who takes this view, states the case for it briefly and well. Nevertheless we recommend the other explanation, and for the following simple reason: the phrase “
and that” (lit., “
and this”) is familiar in N.T. Greek to introduce an
addition of thought, enforcing or heightening what has gone before. See
1Co_6:6;
1Co_6:8; “
and that before the unbelievers;” “
and that, your brethren;”
Php_1:28;
Heb_11:12, (A.V., “
and him, &c.”). But if it here refers only to the general previous idea, gratuitous salvation, it is hard to see what
new force of thought it adds to the words “
by grace.” If on the other hand it refers to the last special statement, “
through faith,” there is a real additional point in the assertion that even the act of believing is a gift of God; for thus precisely the one link in the process where the man might have thought he acted alone, and where therefore, in St Paul’s sense, he might claim to “boast,” is claimed for God. Let the clauses, “and that, not of you; God’s is the gift,” be taken as a parenthesis, and the point of the interpretation will be clear; while the Greek amply admits the arrangement.
That “faith”
is a matter of Divine gift is clear from
e. g. 2Co_4:13;
Php_1:29. Not that a new faculty of trust is implanted, but gracious manifestations—of the soul’s need and the Saviour’s glory—prevail upon the will to choose to repose trust in the right Object. The “gift” of faith is but one phase of the Divine action which (
Php_2:13) “worketh in us to will.” And it may be said to be one aspect of the “gift of repentance” (
Act_5:31;
2Ti_2:25), for repentance is no mere preliminary to faith; it is the whole complex “change of mind” which
includes faith.