This research is focused on a highly effective and untapped feature called gammatone frequency cepstral coefficients (GFCC) for the detection of COVID-19 by using the nature-inspired meta-heuristic algorithm of deer hunting optimization and artificial neural network (DHO-ANN). The noisy crowdsourced cough datasets were collected from the public domain. This research work claimed that the GFCC yielded better results in terms of COVID-19 detection as compared to the widely used Mel-frequency cepstral coefficient in noisy crowdsourced speech corpora. The proposed algorithm's performance for detecting COVID-19 disease is rigorously validated using statistical measures, F1 score, confusion matrix, specificity, and sensitivity parameters. Besides, it is found that the proposed algorithm using GFCC performs well in terms of detecting the COVID-19 disease from the noisy crowdsourced cough dataset, COUGHVID. Moreover, the proposed algorithm and undertaken feature parameters have improved the detection of COVID-19 by 5% compared to the existing methods.