If your population is stratified in two dimensions, eg gender and age group, you should define a separate quota for each possible combination of the two dimensions, as illustrated in this example. Then provided none of the quotas are exceeded, you can never get into the position of having achieved the overall quota for males, but not achieved the quota for males of a particular age-group.
If a characteristic cannot be determined in advance, eg age-group when interviewing strangers in the street, this may sometimes result in a quota being exceeded. It would then be appropriate to eliminate the observation, to ensure that the sample exactly satisfied the pre-determined quotas. Assuming that the quotas are representative of the population, inclusion of additional observations could result in over-representation of some combinations of characteristics, in other words a biased sample, which could easily lead to biased conclusions.