Synecdoche is a literary term used to describe a situation when a part represents a whole. For example, if I asked for "all hands" to be available in a situation, I actually want the entire person's assistance; the "hands" represent the whole of the larger person. Synecdoche isn't a significant factor in determining the meaning of this poem.
Rather, the poem is filled with abstract allusions. As the speaker approaches her house, the image of her husband fills the window as he "looks down" on her like a "lord." This is an allusion to a highly stratified society, conveying her husband's sense of importance and her expected submission to him as his "lady." Likewise, his mouth is compared to an "archer's bow," which might be an allusion to Cupid, found in ancient mythology. It is important to remember that Cupid carried two kinds of arrows—golden arrows, which created desire, and lead arrows, which created feelings of aversion. The uncertainty of this relationship is magnified by the way the couple spends "a long moment / in the truth of [their] situation," one that is laden with suspicion and condescension. For her "lord's" hand is "elegant" and his face is "grandee." The speaker, by comparison, must "run out" for a moment of writing and returns with her "illegal" product hanging like "poached game."
The ending suggests that perhaps the speaker feels that she is like Diana, who was the goddess of wild animals and the hunt. Her poetry, then, demonstrates her own strength and rightful place among deities, who outrank even earthly "lords."