Will people think it strange? Probably. But it is difficult to answer for the "people."
Suffice it to say that the exact search for "grow some gratitude" reveals a mere 29 Google results (including this post), none too convincing.
The more familiar idiom, and the one you are trying to emulate is "grow some balls" (11.5mil hits) or "grow a backbone" (1.5mil). But note that in both these cases the thing that is being grown is, well, a thing, and an organic one at that. I can at least imagine growing a backbone, whereas growing gratitude remains abstract and somewhat nonsensical (despite the compelling alliteration).
If you are using this construction in your writing, I would suggest the far more common, "show some gratitude." Gratitude, an abstract concept, works better with similarly conceptual verbs like "show," "cultivate," or "develop," as opposed to concrete verbs like "grow," "build," or "gather."
I do not suggest the above as a rule, but as a rule of thumb. Good writing is often innovative, but it also follows a certain hidden logic, revealing something new and unexpected about the familiar words and riffing on familiar patterns. Growing gratitude confuses me personally, and I suspect it would sound similarly grating to others.