Ringing effect in time domain reconstructed signal after filtering

Not sure exactly what you did, but in general, in Linear Systems Theory (Fourier Filtering), multiplication in one domain is equivalent to convolution in the other domain. A band pass filter is a rect function and the Fourier Transform of a rect function is a sinc function. So when you multiply by a rect function in the Fourier domain to do band pass filtering, it's like you convolve with a sinc function in the time domain. Since the sinc function has ripples, so will your output signal. Yes this is the Gibbs phenomenon. And since wider in one domain means narrower in the other domain, a wider rect will give a narrow sinc (faster ripples) while a narrow rect will give a wider sinc and slower ripples.