remove outliers in paired samples

Hello friends, excuse the ignorance
I am trying to remove the outliers of a df from a before and after experiment that contains immunoglobulin G levels before treatment and immunoglobulin G levels after treatment, but I can't find a command that removes the outliers before and after (I only find commands to remove outliers in a sample, but I can't apply it since my samples are related)
for example:
H6 has an atypical level before the treatment but after the treatment it may no longer be atypical; however, because it is atypical before the treatment, I must eliminate it along with its corresponding data afterwards.
I wish I had explained well, thank you for your support

The reprex below shows how to illustrate a question to attract more answers. See the FAQ: How to do a minimal reproducible example reprex for beginners.

As a general rule, a data point shouldn't be excluded solely on the basis that it is at the extremes of the range unless there is a sound basis to believe that it represents an outright error—for example a pH value recorded as 16. And indeed the diagnostic plots of an lm model do not show residual outliers or highly influential points.

For the data set imaged, H6 does not appear to be an outlier either before or after treatment. Certainly not compared to H11 and H9. In fact all values are within the conventional 1.75 * interquartile distance.

dta <- data.frame(
  condigo = c("H1", "H2", "H3", "H4", "H5", "H6", "H7", "H8", "H9", "H10", "H11", "H12"),
  iggantes = c(1564, 1434, 1259, 1165, 1293, 1081, 1273, 1360, 890, 1592, 1011, 1251),
  iggdespues = c(1705, 1572, 1233, 1204, 1211, 1187, 1346, 1517, 996, 1584, 983, 1143)

#>    condigo             iggantes      iggdespues  
#>  Length:12          Min.   : 890   Min.   : 983  
#>  Class :character   1st Qu.:1144   1st Qu.:1176  
#>  Mode  :character   Median :1266   Median :1222  
#>                     Mean   :1264   Mean   :1307  
#>                     3rd Qu.:1378   3rd Qu.:1531  
#>                     Max.   :1592   Max.   :1705
par(mfrow = c(1,2))

fit <- lm(iggantes ~ iggdespues, data = dta)
par(mfrow = c(2,2))

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