I use only a 0.08 - 0.1% TFA in water, but I've never used ony water. Perhaps this article may help you: M. Dembek, S. Bocian / Pure water as a mobile phase in liquid chromatography techniques / Trends in Analytical Chemistry 123 (2020) 115793
You need to control the purification by maintaining a low pH to avoid degradation. You may use formic acid or His buffer; all depends on the pI of the peptide.
Late reply, but I use ammonium formate buffer with methanol. Methanol is better able to dissolve the buffer, and using a buffer maintains the pH better than TFA alone (~3.8, in this case). I found that, during purification, the local concentration of some peptides can exceed the concentration of 0.1% TFA causing split or multiple peaks. Buffering at 50 mMol solved the problem. The buffer was required to control the ionization state of the peptide.
You may try buffering at a higher pH, if the pI of your peptide allows it. Using a polymeric reverse phase, you can also use basic buffers.
From my experience without the TFA acid, especially in context to cationic charged peptides, it will impact the elution efficiency and might result in tailing peaks with concurrent decreased in the overall sensitivity.