War.

Ataturk and the Grand National Assembly (basically a re-formed parliament in Ankara) declared the National Pact after the armistice of Mudros and the Greek landings at Smyrna (which mark the start of the Greco-Turkish war.)

The National Pact basically said "we will cede you control of all the Arab territories that were under foreign control at the time of the armistice, but everything else is ours."

As a result of the brief Franco-Turkish war and the troubles they were having in Syria the French decided that they could not plausibly hold both Cilicia (i.e. southern-central Turkey) and Syria. As a result the French effectively renounced their claims to Turkish territory and negotiated the border between French Syria and Turkey which exists to this day (with the exception of Hatay province, which was transferred later).

The British couldn't intervene directly, but backed the Greeks in the Greco-Turkish war. When the Greeks lost, Lloyd George wanted to contest the Straits, but he then lost the 1922 General Election and the new government negotiated the Treaty of Lausanne, which recognized an undivided and unoccupied independent Turkey.