The Eiger Northface trail goes between Alpiglen to Eigergletscher, above Kleine Scheidegg. You do not reach Kleine Scheidegg on the trail, but you can hike another trail down to KS from Eigergletscher.
Are you intending to start hiking in Grindelwald and do a loop? Your intentions are not clear. See this blog for a good description of the trail and your options for start and finish.
https://www.earthtrekkers.com/eiger-trail-hike-bernese-oberland-switzerland/
You can hike one-way if you want, either uphill or downhill. For the downhill hike, you can take the new gondola straight up to Eigergletscher from Grindelwald Grund, and hike down to Alpiglen from there. I did this hike 20 years ago, before the gondola, so we took the Jungfrau train up from KS. We reached KS by gondola from Grindelwald Grund to Männlichen, then walking the Panorama Trail (or whatever they call it now) from Männlichen to KS. That was a nice combination.
Or you could hike the Eiger Northface trail uphill by taking the train from Grindelwald Grund and starting there, hiking to Eigergletscher and returning to Grindelwald by gondola, or walking down to KS and returning to your base by train. We may do that this September, weather depending.
It’s all good.