TFA says they calibrated the buoys data with the ship-based data. The offset is not chosen by hand as you claim, but fitted to make the two types of measurements, which should be measuring the same thing, consistent with each other. That is justifiable to remove systematic errors. Another study by IPCC found the same offset value.
The paper says:
Changes of particular importance include: (i) an increasing amount of ocean data from buoys, which are slightly different than data from ships; (ii) an increasing amount of ship data from engine intake thermometers, which are slightly different than data from bucket sea-water temperatures; and (iii) a large increase in land-station data that enables better analysis of key regions that may be warming faster or slower than the global average. We address all three of these, none of which were included in our previous analysis used in the IPCC report
The details on the calibration are:
First, several studies have examined the differences between buoy- and ship-based data, noting that the ship data are systematically warmer than the buoy data (15–17). This is particularly important, as much of the sea surface is now sampled by both observing systems, and surface-drifting and moored buoys have increased the overall global coverage by up to 15% (see supplemental material for details). These changes have resulted in a time-dependent bias in the global SST record, and various corrections have been developed to account for the bias (18). Recently, a new correction (13) was developed and applied in the Extended Reconstructed Sea Surface Temperature dataset version 4, which we use in our analysis. In essence, the bias correction involved calculating the average difference between collocated buoy and ship SSTs. The average difference globally was 0.12C, a correction which is applied to the buoy SSTs at every grid cell in ERSST version 4.
Second, there was a large change in ship observations (i.e., from buckets to engine intake thermometers) that peaked immediately prior to World War II. The previous version of ERSST assumed that no ship corrections were necessary after this time, but recently improved metadata (18) reveal that some ships continued to take bucket observations even up to the present day. Therefore, one of the improvements to ERSST version 4 is extending the ship-bias correction to the present, based on information derived from comparisons with night marine air temperatures. Of the 11 improvements in ERSST version 4 (13), the continuation of the ship correction had the largest impact on trends for the 2000-2014 time period, accounting for 0.030C of the 0.064C trend difference with version 3b. (The buoy offset correction contributed 0.014C dec1 to the difference, and the additional weight given to the buoys because of their greater accuracy contributed 0.012C dec1. See supplementary materials for details.)
Third, there have also been advancements in the calculation of land surface air temperatures (LSTs). The most important is the release of the International Surface Temperature Initiative (ISTI) databank (14, 19), which forms the basis of the LST component of our new analysis. The ISTI databank integrates the Global Historical Climatology Network (GHCN)–Daily dataset (20) with over 40 other historical data sources, more than doubling the number of stations available. The resulting integration improves spatial coverage over many areas, including the Arctic, where temperatures have increased rapidly in recent decades (1). We applied the same methods used in our old analysis for quality control, time-dependent bias corrections, and other data processing steps (21) to the ISTI databank to address artificial shifts in the data caused by changes in station location, temperature instrumentation, observing practice, urbanization, siting conditions, etc. These corrections are essentially the same as those used in the GHCN–Monthly version 3 dataset (22, 23), which is updated operationally by NOAA’s NCEI. To obtain our new global analysis, the corrected ISTI land data (14) were systematically merged with ERSST version 4 (13), as described in the supplemental materials.
I think TFA does not a good job of conveying this scientific article. They just say "Hey, we 'corrected' our analysis, now what you saw before is gone, believe us now that we did it right". They would be much better to show (1) the raw data, (2) their calibration problem (e.g. temperature measurements of the buoys, how they are offset from the ships), (3) the raw data with the new calibration and finally (4) the new trend compared to the old trend. Poor science communication IMO. I don't see a problem with the study there.