If the pump has just started to leak, the shaft is likely not scored.
That being the case, you should find it easy to replace the two lip seals
(numbers 4 and 10 in the attached illustration).
The sequence is:
1. one or both of the lip seals
passing the lip seal(s) drips out the tell-tale;
dripping warns you to rebuild
the pump (i.e. change the lip seals);
4. if you do not change the lip seals promptly, water may enter where you do not want it to go; and/or
5. stagnant water held against the stainless steel
shaft will cause crevice corrosion
6. grit in water will cause scoring of the shaft.