It's almost always a lot more computationally efficient to convert the points to a grid and apply a conditional grid operator. This assumes--as appears to be the case in the question--that there is at most one point per grid cell (for otherwise the conversion of points to a grid is problematic with Arc* software).
All grid processing frameworks need a way to know the desired output format. Stipulate that in advance: you want the output to have the same origin, dimensions, cellsize, and coordinate system as the original gridded dataset.
ESRI software uses runlength encoding for integral grids. Thus, the conversion of a few scattered points with integral values to grid format will be extremely fast and use little RAM (or disk space if it has to be made permanent). Because even precise precipitation values are rarely given to a greater precision than 1 mm, it can streamline the computation (perhaps a lot) to convert the original grid to integer format and to round the point attribute values if need be. Change the units of measurement if you have to: for instance, if precipitation is in inches, you might convert to thousands of an inch (just multiply everything by 1000 and round). Afterwards it's a simple and fast matter to change the units back to the original ones.