Lately it has been very cold outside (subzero overnight). When starting the car in the morning it seems like the starter wont disengage and make a grinding noise for about a second or two after it has been started. It is fine when outdoor temps are a little bit warmer. Is the starter going bad?
The grease on the shaft the starter drive slides on may be impacted with dirt, and it gets hard when it's cold. That makes its movements sluggish. The fix is to remove the starter, wash off the old grease, and relubricate it with something lighter. Chrysler has a spray chemical called MP-50 that works well. It is similar to WD-40. I prefer a light wheel bearing grease because it sticks around longer and is less likely to evaporate over time than those two spray oils.
Given the nature of the problem, I would be inclined to ignore it. The starter drive has an over-running clutch that slips and prevents the accelerating engine from spinning the starter motor faster. You won't cause damage as long as the starter only takes one or two seconds to disengage.