There are two ways that damage to the starter pinion could have happened: staying engaged after the engine starts (which is what you have suggested) or "milling": trying unsuccessfully to engage when the engine is stationary (i.e. not rotating). To find out which of them occurred you will need to inspect the teeth of the flywheel. If it has been staying engaged, all of the flywheel teeth will show wear marks and/or be partly coated with aluminium. If it has been milling, the only damage to the flywheel will be on the bottom edge of its teeth, mainly in one single area (just before compression). Your picture may be indicating aluminium smeared on the flywheel's teeth, but it's not a great picture - it's up to you to look.
The causes of staying engaged versus milling are quite different. Staying engaged falls into two generic types. Option 1: the starter has been kept energised for a longish period while the engine was running. Option 2: the starter's gear (pinion) has tended to stick on its vertical slide along the starter motor's shaft. Milling, like Option 2, is caused by the pinion not sliding well along the shaft.
If you have aluminium on your flywheel gear (ring gear) the next diagnostic question is whether the over-running clutch (sprag clutch) between the shaft and pinion shows wear. It will be worn if Option 2 is the problem. If Option 1 is the problem the sprag clutch probably won't be worn, but the starter motor itself may show signs of wear, overspeeding, or both.
You have to remove the entire starter motor to work on the pinion. It is secured by the two nuts just below the pinion.
Do not repair the starter until you know what caused the damage. If Option 1 is the problem, the damage may recur unless you find and cure the underlying problem. (The problem may have been some act of stupidity by the former owner, but whatever modification he/she made to the wiring may still need to be fixed).
