Step 1: Understand the phenomenon described.
Garden pea tendrils coil around a support in response to touch.
The movement involves directional growth toward the stimulus.
Step 2: Recall definitions of the given terms.
Thermotaxis: Movement of organisms in response to temperature.
Thigmotaxis: Directional movement of \emph{entire organisms} in response to touch.
Thigmotropism: Directional growth movement of a plant part in response to touch.
Thigmonasty: Non-directional movement in response to touch (e.g., closing of Mimosa leaves).
Step 3: Identify the correct category.
Since tendril coiling:
is a growth response,
is directional,
occurs in plants due to touch,
it is classified as thigmotropism.
Hence, the correct answer is
\[
\boxed{\text{Thigmotropism}}
\]