I am the author of statmod and the remlscore() function. I have never used remlscore to construct confidence and prediction intervals, so I can only say that remlscore() does what it is documented to do.
One could compute confidence intervals for expected values using the standard undergraduate formula for linear regression, but adapted to use the trended variance (phi). Similarly one could adapt the standard undergraduate formula to get a prediction interval for a new observation by plugging in the trended variance estimate.
I guess could get confidence intervals for variances from the estimate standard errors se.gam, but the normality assumption might be poor. Confidence intervals would work better for the log-linear coefficients gamma than for the variance themselves.
Thank you for the reply!