Selecting set number of points within polygon grid cells using QGIS?
You can easily achieve this using function from processing toolbox:
Take grid cell and join its id (or other unique) attribute to related points - Use Join attributes by location and join unique attribute (i.e. "id_grid") from grid layer to point layer. This create new point layer with new attribute - "id_grid" of corresponding grid.
Select only one point per gird - Use Random selection within subsets. As input choose your new layer from step one, for ID Field select "id_grid" and set number required points to be selected (in your case 1)
Extracting to new point layer - Right click on layer, select Save As..., set output parametres (format, CRS...) and check Save only selected features