I think saying neutralizing the aqua regia is the wrong term to use to describe this removal of the free nitric acid oxidizer.
we are eliminating excess nitric acid, the action of acids on the gold would use up most of the acid in forming more neutral salts of gold chloride out of our acid in the reaction, but we will still have excess acid in the solution HCl and any unused nitric, denoxing the solution (evaporating off the excess nitric), will leave us with a metal chloride salt (a dissolved soluble salt of precious metal chloride) dissolved in a little bit of HCl, diluting the solution and letting it sit overnight will let insoluble materials settle, this solution is still slightly acidic (we need it to be slightly acidic for the precipitation process), this dilute chloride solution will not harm the filter paper when filtering.