Convolutional Neural Network (CNN) based deep learning technique is fast gaining acceptability and deployment in a variety of computer vision and image analysis applications, and is widely perceived as achieving optimal performance in detecting and classifying objects/patterns in images. Despite considerable success in various image analysis tasks, several shortcomings have been raised including high computational complexity, model overfitting to the training data, requiring extremely large training image datasets, and above all its black-box style of decision making with no informative explanation. Understandably, the latter is a major obstacle for deployments for medical image diagnostics. Conventional machine learning approaches rely on image texture analysis to achieve high, but not optimal, performances and their decisions can be justified quantitatively. The emergence of the new paradigm of Topological Data Analysis (TDA), to deal with the growing challenges of Big Data applications, has recently been adopted to design and develop innovative image analysis schemes that automatically construct filtrations of topological shapes of image texture and use the TDA tool of persistent homology (PH) to distinguish different image classes. This work is an attempt to investigate the effect of CNN convolution layers on the discriminating strengths of TDA based extracted features. We shall present the effect of the pre-trained filters for the convolutional layers - AlexNet on various PH features extracted from Ultrasound scan images of human bladder for distinguishing benign masses from malignant ones. We shall demonstrate that the condition number of the pre-trained filters influences the discriminatory power of PH representation of certain types of local binary pattern (LBP) texture features post convolution in a manner that could be exploited in designing a strategy of filter pruning that maintain classification accuracy while improving efficiency.