The seven approximately Earth-sized transiting planets in the \object{TRAPPIST-1} system provide a unique opportunity to explore habitable zone and non-habitable zone small planets within the same system. Its habitable zone exoplanets -- due to their favorable transit depths -- are also worlds for which atmospheric transmission spectroscopy is within reach with the Hubble Space Telescope (HST) and with the James Webb Space Telescope (JWST)... We present here an independent reduction and analysis of two \textit{HST} Wide Field Camera 3 (WFC3) near-infrared transit spectroscopy datasets for six planets (b through g). Utilizing our physically-motivated detector charge trap correction and a custom cosmic ray correction routine, we confirm the general shape of the transmission spectra presented by \textbf{\citet{deWit2016, deWit2018}}. Our data reduction approach leads to a 25\% increase in the usable data and reduces the risk of confusing astrophysical brightness variations (e.g., flares) with instrumental systematics. No prominent absorption features are detected in any individual planet's transmission spectra; by contrast, the combined spectrum of the planets shows a suggestive decrease around 1.4\,$\micron$ similar to an inverted water absorption feature. Including transit depths from \textit{K2}, the SPECULOOS-South Observatory, and \textit{Spitzer}, we find that the complete transmission spectrum is fully consistent with stellar contamination owing to the transit light source effect. These spectra demonstrate how stellar contamination can overwhelm planetary absorption features in low-resolution exoplanet transit spectra obtained by \textit{HST} and \textit{JWST} and also highlight the challenges in combining multi epoch observations for planets around rapidly rotating spotted stars. (read more)