It's certainly possible. Liverpool was the second most bombed city in the blitz, and Stoke-on-Trent on the way there and back.

Most of the Liverpool raids took place around Christmas 1940 and then again around May 1941. Did you grandmother say whether it was winter or summer?

If a bomber can't find the target, it still makes sense to drop the bomb. The lighter weight improves cruising speed, and makes for a safer landing.

This happened quite often during WW2 and on all sides. Bombers, which for some reason had missed their target due to navigational errors or bad weather, dropped their loadout on strategically unimportant or minor targets in order save on fuel and increase speed in case enemy fighters showed up.

It's worth noting that Stoke was a coal mining area and had at least one small arms factory operating nearby during the war, in addition to being the major source of pottery and ceramic manufacture in the UK. So it clearly had some strategic value, even if minimal.

Or perhaps the Germans were simply taking out their frustration on the birthplace of the Spitfire's designer.