First, answer your question. Yes, as others have said, I would continue to use it. I actually had a battery that got so hot that a portion of the post (like yours) had partially melted away. In my case, the connect-to-wire connection was not good. I had connectors like yours. I ended up cutting the connector off and getting the battery connectors where you crimp the wire directly to the connector and using those. I used those for three years with no issues.
To me, the wire size and connector for your trolling motor looks too small - but that could be due to size reference in the photo (like fishmen holding their fish as far away from there body as they can - LOL!). I would suggest replacing the battery terminals with these:
Small dab of dielectric and be sure the battery terminal is tight. Good luck.