Set Warnings (Alerts & Thresholds) in MSSQL Replication Monitor using TSQL
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)