GIMP. TIFF. Color profile sRGB IEC61966-2.1 and embedded color profile GIMP - built-in sRGB

Don't convert - at all.

At import tell it not to convert.
At export tell it not to convert.

sRGB IEC61966-2.1 is "industry standard" RGB used for the web. Any time you do colour-space conversion you potentially change the colour balance. If you don't have a fully calibrated system this can make changes you can't even see or know about. Preserving standard sRGB throughout means less margin for error.

In this case, it makes little to no difference, since you would be converting from sRGB to sRGB. At most, you would see a few insignificant-bit flips. (Note: insignificant bit is a technical term.)

If the input file had a different profile, like Adobe RGB, you should convert to sRGB since you plan to use the images on the web.

Do save copies of the unmodified original files.

To demonstrate there is no significant difference:

• Since I do not have copies of your images, I obtained the sRGB v2 color profile from the International Color Consortium website (sRGB2014.icc).

  • sRGB profiles

  I chose this file because the profile you are using says -2.1. There are other versions that may give different results.

• Then I generated a Hald-12 image with ImageMagick. Each pixel in a Hald image is a different color, arranged in a pattern that can used to apply color corrections via lookup table.

  convert hald:12 hald12-0.png
  

• Using GIMP, I exported to the png to hald12-1.bmp, making sure to check "Do not write colorspace information".

• Assigned the color profile sRGB2014.icc to the image.

• Converted to the GIMP built-in sRGB profile.

• Exported the result to hald12-2.bmp.

• Compared results with md5sum. In this case, the conversion resulted in no difference.

  64869fef4a0acf95bea03369d5a89149  hald12-0.png
  6a083813783d9f99a0918c3d97e2364b  hald12-1.bmp
  6a083813783d9f99a0918c3d97e2364b  hald12-2.bmp