You have hit on a common machine tool problem. Grease nipples when rolling element bearings are used. These shouldn't have much grease in them but we are expected to add more from time to time and no way to easily get the old stuff out.
Usually excess grease will go somewhere where it doesn't matter when more is pumped in, This may be achieved by the use of seals which may have perished on old machines.
What I generally do is pump in enough to ensure that what was in has mostly been pushed out. Or dismantle clean everything, examine and replace bearings if needed and start from scratch as far as greasing goes.
If the drill uses a high speed/dc/universal motor and steel gears it's likely to be noisy what ever you do,
John
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