Persistent mild cough after Covid. Help.

Hello Doctors, My father (58 yrs) tested Covid-19 positive on 26 Jul and retested negative on 12 Aug. He had mild cough as symptom initially when we thought of getting him tested. Now, even after a month of tested positive (and then negative) his cough doesn't seems to go away completely. Frequency of cough has reduced but not recovered fully. It is usually when he sits ideal in room, cough frequency is more compared to when he is outside. He says he get this feeling of sore throat and cough makes it relaxing at the moment. He had health checkup done recently, on report except EOSINOPHILS = 13 and Absolute eosinophil count = 715 , other parameters seems to be in normal range. Please clarify what could be the problem. Do we need to get any tests done to identify the actual issue. Please suggest if any medicine/home remedies can help. Thanks and Regards.