I put it back on but is this going to cause any problems? like the thermal compound not working or something?
It would have been best to clean up both surfaces and reapply some more thermal compound but to be honest I find this a contentious issue. Some would say meticulously clean the surfaces and reapply new thermal compond, others would say just clip the thing back on !
In the past I've done both and to be honest I can't see any difference in both practices. However, to ensure the best possible contact between the heat sink and the processor, thereby obtaining optimal thermal transfer, it would have been best to clean it up and apply some new compound. That would be your safest option.