The way to restrict the range of times over which Skyline extracts chromatograms is with the "Min time" and "Max time" settings at:
Settings > Transition Settings > Instrument

Unfortunately, the Instrument time range setting will usually not affect the "Total Ion Current Area" that Skyline reports for the Result Files in the Document Grid. That number comes from looking at the Total Ion Current chromatogram in the raw file, if there that chromatogram is available.

If there is no TIC chromatogram in the raw file, then Skyline instead calculates the TIC area by looking at each of the MS1 spectra and adding up all of the intensities on them. If Skyline ends up doing that, then the time range over which the intensities will be summed will be restricted by the Min Time and Max Time that you may have specified in the Instrument Settings.

I am thinking that Skyline really should respect the Min Time and Max Time numbers when calculating the Total Ion Current Area in all cases.

One way to trick Skyline into not using the TIC chromatogram in the raw file would be to convert the raw file to mzXML. Since mzXML cannot store chromatograms, Skyline would be forced to calculate the TIC the old way by summing intensities on individual spectra. This is probably not a good way to do things since mzXML loses other information about maybe how wide of a window around the precursor was isolated and what m/z range was scanned by the instrument.

If you have some other way of calculating the TIC area, you can tell Skyline to use that number for normalization. For instance, if you have some other software that will tell you what those areas are, you can type them into the Document Grid. In the Document Grid, there is a number called "Explicit Global Standard Area" where you can type the number that you want Skyline to use for normalization. Then, you can set the normalization method at "Settings > Peptide Settings > Quantification" to "Ratio to Global Standards" and Skyline will use that number for normalization.

Can you send us your Skyline document and one of your raw files?
In Skyline, you can use the menu item:
File > Share
to create a .zip file containing your Skyline document and supporting files including extracted chromatograms.

If that .zip file and your raw file are less than 50MB you can attach them to this support request.
You can upload larger files here:
https://skyline.ms/files.url

-- Nick

Dear Nick,
First of all, many thanks for your post!
I tried to change “Min time” and “Max time” as you suggested however, at least in my hands it didn’t change the “Total Ion Current Area” that Skyline reports.

Unfortunately, I do not want to convert the files to any other format. The idea is to streamline the process of quality control so that with little additional effort we can follow whether the regular samples that we run are not much different from each other (within a single project). Therefore, we want that the software (in this case Skyline) to do the most work for us (ideally "on the fly"). Alternative that someone suggested me would be to use ProteoWizard (msconvert) and during conversion set the scan time range. But we also want to avoid that.

Thank you so much for help!

I attached the Skyline document that we used so far for monitoring MSQC.
I also uploaded one raw file 220203_zmHF_Hela_50ng-01-MQLive to the URL you provided. Just an example.