I've had a look at the Nature paper you reference. It is not persuasive. Look at their Figure 4a, and try to ignore their fitted curves. What do you see?
I see highly variable data, which is clearly auto-correlated. And indeed the paper discusses how ENSO and NAO are correlated with the measurements, which is a reason to expect strong autocorrelations. As far as I can see, none of their error bars or significance tests account for autocorrelation. So you should ignore them.
Just eyeballing the data points does not give any clear impression of a decline over time. Consider the four regions with the most early data. Arctic has values around 1930 comparable to the most recent, and no clear indication of a trend, either long term, or in recent decades. North Atlantic has early values around 1910 that are lower than recent values, and again no sign of a trend. North Pacific seems trendless as well, with any slight indication of a downward trend not significant in view of the autocorrelation. Only Equatorial Pacific could be seen as showing a declining trend, but it is also the most variable, with some very high points (as well as lower points), with the high points all before 1960. One might wonder whether the high points represent measurement anomalies.