In Tim O'Brien's short story "The Things They Carried," what recurring motif reminds Lieutenant Jimmy Cross of home?

I'm assuming that you're talking about Tim O'Brien's short story "The Things They Carried," as opposed to the full length novel of the same name. 
 
In this case, the answer to your question would be Martha. 

The title of the story refers not only to the actual equipment that soldiers carry, but also to the memories, hardships, and trauma they must hypothetically "carry" with them for the rest of their lives. 

While Lieutenant Cross carries both a rucksack and gear, these objects are not recurring motifs. They don't represent anything other than what they are.

Martha is a girl from back home for whom Cross has feelings. Martha and Cross are not in a relationship, but Cross thinks about Martha both romantically and sexually, and the idea of her is what keeps him going while in Vietnam. 

In fact, the story's opening is dedicated to introducing Martha. It reads,

"First Lieutenant Jimmy Cross carried letters from a girl named Martha, a junior at Mount Sebastian College in New Jersey. They were not love letters, but Lieutenant Cross was hoping, so he kept them folded in plastic at the bottom of his rucksack" (O'Brien). 

Throughout the story, Martha comes up time and time again. The narrator even explains that Cross humped (military slang for "carried") his love for Martha with him wherever he went. 

At one point, the narrator says, "Almost everyone humped photographs. In his wallet, Lieutenant Cross carried two photographs of Martha" (O'Brien).
 
Basically, Martha, and everything she encompasses (home, civilian life, love), is a recurring motif in the story. In fact, Cross becomes so distracted while thinking about Martha that, at one point in the story, one of his men is shot and killed because he was thinking about Martha instead of looking out for him. 

After that, Cross burns the letters from and photographs of Martha. He then decides to give up all the fantasies he has about the two of them ending up together.
 
The narrator goes on to say, "This was not Mount Sebastian, it was another world, where there were no pretty poems or midterm exams, a place where men died because of carelessness and gross stupidity" (O'Brien). 
 
So, yeah; if there's one, main recurring motif in the story, it's definitely Martha and all she represents.