Set Warnings (Alerts & Thresholds) in MSSQL Replication Monitor using TSQL How can I configure the settings on this screen in Replication Monitor using TSQL?

For reference, we're on SQL 2014.
Detailed information about programmatically monitoring replications can be found on the official Microsoft Docs site:

Reference: Programmatically Monitor Replication

There is detailed information on all the stored procedures required to query monitoring details:

To monitor Publishers, publications, and subscriptions from the Distributor


sp_replmonitorhelppublisher
sp_replmonitorhelppublication
sp_replmonitorhelpsubscription


To monitor transactional commands waiting to be applied at the Subscriber


sp_replmonitorsubscriptionpendingcmd


To monitor merge changes waiting to be uploaded or downloaded


At the Publisher: sp_showpendingchanges  


  returns a result set showing information on changes that are waiting to be replicated to Subscribers  

At the Subscriber: sp_showpendingchanges  


  returns a result set showing information on changes that are waiting to be replicated to the Publisher  



To monitor Merge Agent sessions


sp_replmonitorhelpmergesession (either at the subscriber or distributor)
sp_replmonitorhelpmergesessiondetail (either at the subscriber or distributor)


Answering your question

The stored procedures required to read or change the monitoring thresholds are the sp_replmontirohelppublicationthresholds and sp_replmonitorchangepublicationthreshold procedures.

To view the monitor threshold metrics for a publication


sp_replmonitorhelppublicationthresholds



sp_replmonitorhelppublicationthresholds 
          [ @publisher = ] 'publisher'  
        , [ @publisher_db = ] 'publisher_db'  
        , [ @publication = ] 'publication'   
    [ , [ @publication_type = ] publication_type ]   
    [ , [ @thresholdmetricname = ] 'thresholdmetricname'  



The parameters are:

@publisher        : the name of the publisher
@publisher_db     : the name of the published database
@pbulication      : the name of the publication
@publication_type : 0 = transactional publication
................    1 = snapshot publication
................    2 = merge publication  

To modify the monitor threshold metrics for a publication


sp_replmonitorchangepublicationthreshold  



sp_replmonitorchangepublicationthreshold 
          [ @publisher = ] 'publisher'  
        , [ @publisher_db = ] 'publisher_db'  
        , [ @publication = ] 'publication'   
    [ , [ @publication_type = ] publication_type ]   
    [ , [ @metric_id = ] metric_id ]   
    [ , [ @thresholdmetricname = ] 'thresholdmetricname'   
    [ , [ @value = ] value ]   
    [ , [ @shouldalert = ] shouldalert ]   
    [ , [ @mode = ] mode ]  



The parameters are:

@publisher        : the name of the publisher
@publisher_db     : the name of the published database
@pbulication      : the name of the publication
@publication_type : 0 = transactional publication
................    1 = snapshot publication
................    2 = merge publication
@metric_id        : 1 = expiration
................    2 = latency
................    4 = mergeexpiration
................    5 = mergeslowrunduration
................    6 = mergefastrunduration
................    7 = mergefastrunspeed
................    8 = mergeslowrunspeed
@thresholdmetricname: the name of the publication threshold
................      (either this parameter or @metric_id is required)
@value            : the new metric value
@shouldalert      : generate alert (1=yes;0=no)
@mode             : monitoring mode (1=on;2=off)