Before answering, it helps to know what is in the file. A photograph from a phone typically carries an EXIF block: camera make and model, settings, orientation, a timestamp, and often the GPS coordinates of where it was taken. None of that is visible in the image, and all of it travels with the file.
The short answer
Yes. Compressing through a browser decodes the image into raw pixels and encodes a new file from those pixels. The EXIF block is not carried across, because the encoder is given pixels, not the original file. What comes out has no camera information, no GPS and no original timestamp.
This is a side effect of how the compressor works rather than a separate feature, and it is worth knowing which way it cuts: it is good for privacy and bad if you were relying on that metadata being preserved.
What is lost that you might miss
- Orientation. Phones often store the image sideways and record a rotation flag. The compressor applies the rotation while decoding, so the pixels come out upright and the flag is no longer needed.
- Timestamps. The original capture time is gone. The file's modified date becomes the time you saved it.
- Camera and lens details. Gone.
- Colour profile. Depends on the browser. A wide-gamut image may end up described in sRGB, which can shift saturated colours slightly.
What is not lost
The visible image. Compressing changes how much detail is kept, not what the picture is. For a moderately compressed file the difference at normal viewing size is usually impossible to see.
When you want to keep the metadata
If the EXIF block is the point - a photography portfolio, an archive, a file that must prove when and where it was taken - do not re-encode it. Copy the file instead. Compressing and then restoring metadata by hand is more error-prone than simply keeping the original.
When removing it is the point
Posting a photograph of your home, your children or a document on a desk. The GPS coordinates in an untouched phone photo can identify a street address. Re-encoding is an easy way to strip that before the file leaves your device, and it happens locally: the compressor never uploads anything. The privacy policy covers what the site does and does not record.
One caveat worth stating plainly: removing EXIF does not make a photograph anonymous. Visible details, reflections and backgrounds identify people far more often than metadata does.