u r giving yourself 3 problems....1) yes u will lose some wax but this is not the end of the world, 2) how will u clean wax out of the carpet - if the carpet is important, wax in the carpet just attracts more dirt, 3) u will get fibres from the carpet onto the base of the ski and it is the same as dirt / junk and u don't want to put a hot iron on it and melt / burn it in.
so the most important issue is the junk and dirt and microscopic stuff from the carpet that may stick to ur bases. Wipe it off or Ski it off. Brush it off or scrape it off before u tune /wax again. After u clean the skis do what some perfectionists do - a hot wax scrape. Use a warm melt wax (cheap) and melt it on and while it is still sft and liquid on the ski base scrape it right off. All the dirt is in the melted wax so off it comes...then do a "real" wax.
I hope there is no sand / stones or sharp dirt in the carpet.