Gratitude?

Χαιρετε!
On page 119 of Unit 14 of Dr. Mastronarde’s Introduction to Attic Greek, he states at the bottom of the page, “Χάρις
in the sense of gratitude is used in various verbal idioms, such as Χάριν ἔχειν . . .”

He gives an example, ““τούτοις τοῖς θεοῖς χάριν τῶν καλῶν δῶρων ἔχομεν.”
He did not decline χάριν, but he did change ἔχειν to ἔχομεν..” So I guess the noun remains the same in this construction and the verb gets declined?

χάριν is declined, since it is accusative of χάρις. I guess you expected a χάριτα, but the most common form is χάριν.
On the other hand, finite forms of verbs are not declined but conjugated (ἔχομεν).

I thought χάριν would be in the nominative. I am confused as to why it is an accusative?

The nominative is the subject case, the accusative the direct-object case. We (subject) have gratitude (direct object). Hence, the accusative.

So χάριν is the object of ἔχομεν?

Yes, it is.

Ευχαριστώ!

Note that χάρις is irregular. In the singular:

N. χάρις
G. χάριτος
D. χάριτι
A. χάριν

You are asking good questions and making progress…