Here I put the improved Dario’s idea to clear the selection and quantities during the order process.
By using Checklist option we can make it but we lose the image/photo associated to product on the way. That is the reason to use a 2nd Inline List.
Sorry for the ping pong effect which causes these rare problems with the selected quantities and products! A terrible problem that needs to be eliminated as soon as posiible. @Mark helps us 
Saludos @Tuttografica