This issue is not reproducible in ArcGIS Pro 3.0.3 and 3.1_41787.
Use this code with the respective owned data path [below is the actual successful run from 3.0.3 with the results].
import arcpy
from arcpy import env
arcpy.management.MakeMosaicLayer(r"D:\data__for Issues\11__3.1\gp_\BUG-000154226\jacobsDataVersion\RasterTestingBUG.gdb\TestBigRaster", "BigRasterMosaicLayer")
arcpy.management.SelectLayerByLocation('BigRasterMosaicLayer\\Footprint', 'INTERSECT', 'county', "", "", 'NOT_INVERT')
arcpy.management.RemoveRastersFromMosaicDataset("BigRasterMosaicLayer", "Name = 'Banning'", "UPDATE_BOUNDARY", "MARK_OVERVIEW_ITEMS", "DELETE_OVERVIEW_IMAGES", "DELETE_ITEM_CACHE", "REMOVE_MOSAICDATASET_ITEMS", "UPDATE_CELL_SIZES")
Additionally, please consult the Remove Rasters From Mosaic tool help documentation. Usage tip for the following information:
https://pro.arcgis.com/en/pro-app/latest/tool-reference/data-management/remove-rasters-from-mosaic-dataset.htm
Usage
• There must be a selection or a query specified; otherwise, the tool does not run. To delete all the records from the mosaic dataset, specify a query that would select all the rasters, such as 'OBJECTID>=0'.