Extracting the posterior mean and covariance from the object created by "GP" in GaussianProcesses.jl

As part of a broader Value Function Iteration exercise, I wish to feed the output of predictMVN or predict_f back into an instantiation of GP.
Suppose we have created an instance gp by feeding GP the usual ingredients: training data x1, target data t1, along with eg MeanPoly(B) and a suitable kernel kern.

How do I now extract the posterior mean and covariance from gp and, moreover, extract them as Mean and Kernel?

Or would this question be best posted on the GitHub repository?