Final answer:
The sense of smell is the sensory input not relayed by the thalamus; olfactory signals are sent directly to the olfactory cortex without thalamic mediation.
Step-by-step explanation:
The sense that is not relayed to other parts of the brain by the thalamus is the sense of smell. The thalamus acts as a sensory relay station for all other senses such as vision, hearing, touch, and taste.
However, olfactory information bypasses the thalamus and is instead relayed directly to the olfactory bulbs and then to the olfactory cortex for processing.
This is unique among the senses because the olfactory system has a direct connection to the cortex, which is not mediated by the thalamus.