This was the basis of my final paper during my undergrad, well it was more about the "creation and effect on interwar German-Polish relations" (to quote my title). And in short, not at all.
First off it has to be noted that Poland never legally controlled Danzig. It was a Free City, nominally under control of the League of Nations but with economic ties to Poland. So even if the Poles wanted to give up the city (which they most certainly did not), they never owned it and thus couldn't.
One of the key demands of the Poles during the Paris Peace Conference was that they be given unimpeded access to the sea; they would not accept Germany to retain all the territory bordering the Baltic Sea, fearing that in the event of hostilities they would be barred from accessing it, and so wanted their own borders to reach the sea (and indeed an early German proposal of this calibre was rebuffed, with Lloyd George arguing that if the Germans felt it good enough for the Poles, it could work for the Germans).^1 This of course was opposed by the Germans, who would thus see East Prussia cut off from the rest of Germany, not to mention that the most logical choice, Danzig, was ethnically German (at the time 96% of the population identified as German).^2 In an attempt to rectify this, the Allies created a solution that "satisfied none of those directly concerned^3: the Free City of Danzig. Though nominally a sovereign state, it was in a customs and economic union with Poland, who also controlled its foreign affairs and had unrestricted use of the port, as well as the ability to place a small military force within the city (at Westerplatte, where the first shots of the Second World War were fired).
Fearful that the status quo would not last, Poland began in 1924 to turn Gdynia, a fishing village a few kilometres from Danzig (but located entirely within Poland) into a viable alternative. Both Danzig and Germany argued this violated the treaty establishing the city, and thus it should have been allowed to return to Germany; this argument was denied by the League.
The rise of Hitler saw renewed efforts to bring the city back into German control. At one point he had even remarked to Józef Beck, the Polish foreign minister, that "Danzig is German, will always be German, and will sooner or later become part of Germany."^4 However for various reasons it was not until 1938 that Hitler undertook serious efforts to reclaim Danzig. Various proposals were made to Poland, including extending the non-aggression pact signed in 1934, renouncing other territorial claims, and various other things; all were turned down (while the Poles didn't have control over the city, if they conceded to something the League would have signed off on it). Negotiations actually lasted until late August, 1939, but seeing how the Munich Agreement had turned out the Poles were less than interested in German proposals. Beck at one point even said to his German counterpart von Ribbentrop that "any other solution, and in particular any attempt to incorporate the Free City into the Reich, must inevitably lead to conflict."^5
For some further reading on the city itself, there are some older books on the subject:
Christopher M. Kimmich, The Free City: Danzig and German Foreign Policy 1919 – 1934. New Haven, Connecticut: Yale University Press, 1968.
Herbert S. Levine, Hitler’s Free City: A History of the Nazi Party in Danzig, 1925 – 39. Chicago: University of Chicago Press, 1973.
John Brown Mason, The Danzig Dilemma: A Study in Peacemaking by Compromise. Stanford, California: Stanford University Press, 1946.
Casimir Smogorzewski, Poland’s Access to the Sea. London: George Allen & Unwin, 1934.
There are also some contemporary journal articles that look at the city; I haven't included them here, but can do so if requested. Other works on the subject of interwar Germany, Poland, the League of Nations, and so forth also often touch on Danzig, and look at the issue as well.
Notes: