Match unpaired points between two sets
This is called the Assignment Problem, or equivalently Weighted Bipartite Matching.
You need a way to compute a numeric distance or cost between any point in C and any point in T (it sounds like you already have this). Create a graph with a vertex for each point in C, and a vertex for each point in T, and an edge between every pair of vertices from different sets (i.e., one from C, one from T) having weight equal to the cost between them, and run one of the several algorithms described on that page, e.g., the Hungarian algorithm, which can be implemented to run in $O(n^3)$ time though the description on that page is only $O(n^4)$. As this might be tricky to implement, I would suggest instead setting up a linear program and using a freely available LP solver to solve it.