Why did Batumi stay with Georgia after Turkey took back Kars?

Why didnt the turks take the whole territory that they lost to Russia just a few decades ago, given that the region was majority muslim?
 
After a temporary occupation by Turkish and British troops in 1918–1920, Adjara became part of the Democratic Republic of Georgia in 1920. After a brief military conflict in March 1921, Ankara's government ceded the territory to Georgia under Article VI of Treaty of Kars on the condition that autonomy be provided for the Muslim population. The Soviet Union established the Adjar Autonomous Soviet Socialist Republic in 1921 in accord with this clause. Thus, Adjara was still a component part of Georgia, but with considerable local autonomy.
https://en.wikipedia.org/wiki/Adjara
 
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