-다 is short for -다가, so 넣었다 뺐다 하다 is putting something in and taking it out again, over and over — a USB stick, a brush, bags, something into a toaster. Every line here is that back-and-forth. 줬다 뺐다 하다 is the unkind version: offering something and snatching it away as the other person reaches for it.