you can edit your alignments as you like with, for instance, Jalview (http://www.jalview.org/).
To answer your question whether or not cutting 20 residues will affect the alignment, I need to know: (1) do these 20 aa align? (2) how long are your sequences, so which part of the whole peptide the 20 residues make? and (3) why are they "unwanted"? If "unwanted" means that they are just unaligned short "tails", you can remove them without big doubts, it most likely will not influence the results of the alignment but will improve its overall quality.
The procedure of alignment editing is in general legal, so there's nothing wrong in doing so, and there are tools to do it automatically, for instance, GBlocks and TrimAL. You can check them.
For your clarification, The protein of interest is 208 aa in size but nearly 20-30 residues of c-terminal, being alone (unaligned) when aligning with other othorologus. Also they are not actively involve in the any kind of activity (out of the functional domain).
My question is "will it effect the scoring of the alignment and make any misalignment while we removing the residues?"
no, there will be no misalignment. The overall scor of the alignment will change but this is not important in practice. You can actually just try and see what happens. The alignment will not become worse. You can try to apply the tools which I recommended to you and select the alignment that fits your aims better. What do you need the alignment for ? If for phylogeny reconstruction, all these editing things can affect it very strongly.
Yes, you can trim the later part of your sequence, generally manual adjusting of a multiple sequence alignment is done to improve your phylogenetic tree.
If you trim the ends after aligning all the sequences, it generally does not affect the analysis, rather if the ends are too short for some of the sequences and too long for the others, it is always advisable to trim them, rather continuing with gaps for a phylogenetic tree construction.