This is not an inconvenient data problem. That the ends of past ice ages were not caused by a rising atmospheric carbon dioxide concentration but instead caused it with some lag does not at all proof that a rising atmospheric carbon dioxide concentration can not cause rising atmospheric temperatures.

For example - completely made up - a change in the orbit of the earth could cause rising temperatures and therefore the end of an ice age. This could then free carbon dioxide trapped in or under the now melting snow and ice and in turn this change in the composition of the atmosphere could additionally contribute to the rising temperatures.